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Calculus: Derivative Problems

** Please see the attached file for the complete problem description ** 14. f(x) = (x^3 + 2x+ 1) (2+ (1)/(x^2)) Find derivative 34. Suppose f and g are functions that are differentiable at x = 1 and that: f(1) = 2 f prime (1) = -1 g(1) = -2 g prime (1) = 3 Find the Value of h prime (1) for : h(x

Implicit differentiation applied

Calculate dz/dx using implicit differentiation. given the equation: (e^(2xy)) + z - (x^2)sec((y)(z^2)) = 2 **note: {the d is the cryllic, or curly d...signifying the partial of z with respect to the partial of x}

Differentiation of Algebraic Functions

Please see attached for proper formatting. 1. Find the 2nd derivative of g(x)=x^2/(x^2 + 1) . 2. Find d^3/dx^3 (7x^3 - 8x^2 + 2x) . Use differentials to approximate the following: 1. (127)^(1/3) 2. sin 31°

Problems Involving Differentiation of Algebraic Functions

THE DIFFERENTIATION OF ALGEBRAIC FUNCTIONS Use implicit differentiation to find the dy/dx: 3xy + x2y2 = 1 xy1/2 - 2x + y = 8 (x + y)3 = x3 + y3 3y2 + 5x2 -2x = 5 y4 = x3y2 + x2y3 - 3 Find the indicated higher order derivative of the following functions: 1. Find the 2nd derivative of f(x) = 7x^5 - 4

Differentiate, Find the area of the section of the hyperbola

Please show work step-by-step so that I can understand the process. 1. Differentiate... 4. Differentiate... 19. Find the area of the section of the hyperbola (x/a)^2 - (y/b)^2 = 1 that is bounded by the curve and the line x = 2a. Please see attachment for more questions.

find these derivatives

1. On one occasion the gremlin tried to take over the kingdom with a bacteria dish. The bacteria multiplied at such a rate that . At hour, the number of bacteria was 10. If the gremlin had not been stopped, how long would it have been before equaled 1000? For problems 2 thru 8, find . 2. 3. 4. 5.

Instantaneous Rate of Change of h with Respect to x

The altitude h (in meters) of a jet as a function of the horizontal distance x (in kilometers) it has traveled is given by: h=0.000104x^4 - 0.0417x^3 + 4.21x^2 - 8.33x Find the instantaneous rate of change of h with respect to x for x = 120 km.

Determine Largest and Smallest values of the Marginal Cost

The total cost of producing x units of a certain commodity is C(x) = 2x^4 - 10x^3 - 18x^2 + 200x + 167. determine the largest and smallest values of the marginal cost for 0< X 5.. i cant put the equal sign by the < point, but both are equal or greater or equal to or less.

partial fraction expansion

Determine the constants A, B and C in the partial fraction expansion of the given expression. Explain how you got them. (z+1)/(z^2 (z-1) ) a. by Partial fractions method. b. by differentiation. c. by assigning numerical values to z.

Application of derivative functions

For the function below, find a) the critical numbers, b) the open intervals where the function is increasing, and c) the open intervals where the function is decreasing. f(x) = 2.6 + 2.4x - 0.7x^2 b and c should be in interval notation.

Slope of a tangent line and derivatives

Find the slope and the equation of the tangent line to the graph of the function at the given value of x. f(x) = x^4 - 5x^2 + 4 x = -2 The slope of the tangent line = ? The equation of the tangent line is y= ?

Limits and Derivatives

1. Find the following limits. a) Limit as x approaches 3 of: (x^2-x-6)/(x-3) b) Limit as theta approaches 0 of: (sin(3 theta))/(sin(5 theta)) 2. Using definition of derivative find the derivative of: a) f(x)= 4x^2-6x-5 b) f(x)= (1-x)/(x+1) 3. Differentiate and simplify: a) y=cos

Find the derivative of the following functions.

Question 5a. Find the derivative of the following functions: i) f(x) = 3 ln(x) / x^2 ii) f(x) = 3 x^2 ln(2x) iii) f(x) = ln(3 x^2 - 2 x + 1) iv) f(t) = e^2t ln(t + 1) Question 5b. A car is 30 miles north of town, heading north at 25 miles per hour. At the same time, a truck is 40 miles east of town, traveling east at 50

Finding a derivative by implicit differentiation

Question 3: a) Find the derivative of the following functions dy/dx, by the method of implicit differentiation: i) (x^2)(y^2) - xy = 8; ii) sqrt(x + y) = x; iii) (x - y)/(2x + 3y) = 2x. b) Find the equation of tangent line to the graph of the following function at the indicated points: i) y^2 - x^2 = 16; at (2, 2 sqrt(5); i

4 small questions

Please show all work 1)It has been conjectured that a fish swimming a distance of L ft at a speed of V ft/sec relative to the water and against a current flowing at the rate of U ft/sec (u<v) expends a total energy given by: E(v)= aLv^3/v-u where E is measured in foot-pounds (ft-lb) and a is a constant. Find the speed V

Maximization application: Printer example problem

A printer is making a poster that will have a total area of 200 square inches and will have 1 inch margins on both sides, a 2 inch margin on the top and a 1.5 inch margin on the bottom. What dimensions will give the largest printed area? Or, what is the area of the printed region inside the margins?

Partial Derivatives using Chain Rule

Need help finding partial derivatives of attached problems. Find three partial derivatives of the function r with respect to x, y, and z 1. r = uvw &#8722; u^2 &#8722; v^2 &#8722; w^2 where u = y + z, v = x + z,w = x + y 2. r = p / q + q / s + s / p where p = e^yz, q = e^xz, s = e^xy

Lowest Flying Speed: Finding the Derivative

The lowest flying speed v (in ft/s) at which a certain airplane can fly varies directly as the square root of the wing load w (in lb per sq. ft). If V=88 ft/s when w= 16 lb/sq ft, find the derivative of v with respect to w. Please show work. Thanks

Instantaneous rate of change of solar radiation

The total solar radiation H on a particular surface during an average clear day is given by: H=5000/T^2+10 where t (-6 < equal to or less than t < equal to or less than 6 ) is the number of hours from noon. Note that 6 a.m. is equivalent to t = -6. Find the instantaneous rate of change of H with respect to t at 3 p.m.

Derivatives: Example Clock Problem

If the minute hand and the hour hand on the clock both start at 12:00 when will the two hands first coincide? How many times will they coincide in 12 hours? Please solve with the means of derivatives, show and explain all steps.

Finding the derivative of a function


Slope of a tangent line and derivatives

Find the point on the graph of the given function at which the slope of the tangent line is the given slope. f(x)= (x^3) + (9x^2) + 36x +10 slope of the tangent line = 9 What is the ordered pair?

Give an example...

A) Give an example of a function where the derivative does not exist in at least one point. b) Write a formula for this function. c) For your function, at which point(s) does the derivative not exist? In words, explain why the derivative does not exist here.

Partial derivatives and price elasticity

1. Determine the partial derivatives with respect to all of the variables in the following functions: a. b. 2. A company hires you as the marketing consultant to estimate the demand function for its product. You have concluded the demand function is Where Q is the quantity demanded per capita pe

Concentration of Drug: Increases, Decreases & is Most Effective

The percent of concentration of a drug in the bloodstream x hours after the drug is administered is given by the function: K(x) = 4x/(3x2+27) a) On what time intervals is the concentration of the drug increasing? b) On what intervals is it decreasing? c) When is the drug most effective? You must show all steps, the e

Use chain rule for the first three derivatives of cos^2(2x)

I need to know how to find first 3 derivatives for f(x) = cos(sq) 2X. I am able to find derivatives for similar problems, but the 2X portion is throwing me off. Any assistance you can provide will be greatly appreciated. Please explain how to similar problems with a coefficient in front of the variable.

Find the derivative in Calculus

Find the derivative; G(v)= (v^3-1)/(v^3+1) Find the limit; lim(sin3x)/(sin5x) x->0 Find the derivative; R(w)= (cosw)/(1-sinw) H(o)=(1+seco)/(1-seco) Find the derivative; F(x)= cos(3x^2)+{cos^2}3x N(x)=(sin5x-cos5x)^5 "Assume that the equation determines a differentiable function f such that y=f(x),

Generating Functions: Example Problem

Let a(subn) equal the number of ternary strings of length n made up of 0s,1s,and 2s, such that the substrings 00,01,10, and 11 never occur. Prove that a(subn)= a(subn-1) + 2a(subn-2), (n>=2) with a(sub 0)=1 and a(sub1)=3 Then find a formula for a(sub n)

Constant second set of differences for unit input increment

Prove that if f(x)= ax^2 + bx + c , then if the input goes up by one then the second set of differences will be constant and the constant will equal (2!)a. Think about how to prove this in general. Do not make unnecessary assumptions about any initial input.