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# Derivatives

### get the first derivative of N

Initial equation - 100 +10B + 20N - B2 - N2 + 0.5 BN ( B2= B to the secondpower and N2 equals N to the second power) I want to get the first derivative of N so I got this far: 10-2b + .5n =0 .5n=2b -10 N= 4b -20. I can't figure out how they got the answer for N ? Also, why is the number 10 without the B when

### Differentiation Calculation Functions

Can you please show me how to calculate the following 1. Differentiate f(x) = 1n(5x - 7) with respect to x 2. Obtain the derivative of f(t) = 1n( 5 - 2/3 t)

### Differentiation ( Derivative ) : y=3/(1-X^2)^1/3

Differentiate ( find the derivative ) : y=3/(1-X^2)^1/3

### Derivatives of Logarithmic and Exponential Problems

Differentiate each of the following functions with respect to the appropriate variable: 1. f(x) = ln(7-5x) 2. y(x)=e^(4x-5) 3. f(x) = ln(x- 3/7 t) 4..... Please see the attached file for the fully formatted problems.

### Derivatives: Relative Minimum or Maximum

Please show that the function f(x) = ln(x) does not have a relative minimum or relative maximum. Please show that for a polynomial of degree 3, if 1 + i is a zero, then 2 + i is not a zero.

### Hyperbolic Functions : Numerical Values (11 Problems), Limits (9 Problems) and Derivatives (12 Problems)

Find the numerical version of each expression 1) sinh 0 2) cosh 0 3) tanh 0 4) tanh1 5) sinh1 6) cosh1 7) sech 0 8) sinh(ln 2) 9) cosh(ln3) 10) cosh^-1 1 11) sinh^-1 1 Use definitions of hyperbolic functions to find each. 1) lim as x approached infinity tanh x 2) lim as x approached infinity sinh x 3) lim a

### Inverse functions

Please see problems and show step by step solution in detail please. --- 7.4 Inverse functions Differentiate the problems: 1) f(x) = ln(x^2 + 10) 2) f(à?) = ln(cos à?) 3) f(x) =log2(1-3x) 4) f(x) = 5thROOT(ln x) 5) f(x)=SQRTx * (ln x) 6) f(t) = ln [(2t+1)^3 / (3t-1)^4] 7) h(x)=ln(x + SQRT(x^2-1)) 8) g(x)=ln[(

### Find the derivative of a function : (x-3)^2 / [(x^2)+1] ^2

(x-3)^2 / [(x^2)+1] ^2

### Derivative of inverse trig function

How do you solve: y= sec&#8254;¹ 5s

### Derivatives of inverse trig functions

How do you solve: y= cos&#8254;1 (1&#8725;x)

### Derivative

1.) compute the derivative of f(x)= arctan (x^2) 2.) compute the derivative of f(x)= ln(x^2/(2+x)) 3.) determine an equation for the line tangent to the graph of y= xe^x at the point on the graph were x=2

### Differentiation

F'(y) if f(y)=exp ( 3 - 1/4 y )

### Derivatives, maxima, minima

1. Find the derivative: f(x) = (x^3-8)^(2/3) 2. Write and equation of the tangent line to the graph of y = f(x) at the point on the graph where x has the indicated value. f(x) = (3x^2 + 5x + 4)(4x + 3), x=0 3. Find the values of any relative extrema: f(x)=1/(x^2-1)

### Differentiation Function

-kt f'(t) if f(t)=G(1-e ) Note (-e is to the square of -kt)

### Differentiation Functions

1 f'(y) if f(y) =exp(3- 4 y)

### Distance of a body from a point is given by a function

Distance of a body from a point is given by s=xsin(at+b) . Show that the velocity and acceleration are given by v=xacos(at+b) and b=-a(squared)s

### Application Word Problem: Continuity and Derivatives

It costs Sugarco 25 cents/lb to purchase the first 100 lb of sugar 20 cents/lb to purchase the next 100 lb and 15 cents to buy each additional pound. Let f(x) be the cost of purchasing x pounds of sugar. Is f(x) continuous at all points? Are there any points where f(x) has no derivative?

### Derivatives and Maximum Volume :... sum of its length and girth (distance around) does not exceed 108 in. What dimension will give a box with a square end the largest possible volume?

The U. S. Postal Service will accept a box for domestic shipment only if the sum of its length and girth (distance around) does not exceed 108 in. What dimension will give a box with a square end the largest possible volume? Show your work.

### Find the derivative of f(x) =ln(5x-7) with respect to x.

Differentiate f(x) =ln(5x-7) for x.

### Differentiation : Find the derivative

Obtain dy dx y=(2+3x)^-0.6

### Differentiation : Find the derivative of Y=(5X+4)^3

Y=(5X+4)^3 What is dy/dx?

### Differentiation

Please solve and explain. Two factories are located at the coordinates (-x,0) and (x,0), with their power supply located at (o,h). Find y such that the total amount of power line from power supply to the factories is a minimum.

### Differentiation

A rectangular package can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume. Assume cross section is square.

### Maximum area with given perimeter

A Norman window is constructed by adjoining a semicircle to the top of a rectangular window. Find the dimensions of the Norman window of maximum area if the total perimeter is 16 feet.

### Differentiation

Use a graphing utility to graph f and g in the same window and determine which is increasing at the faster rate for "large" values of x. What can you conclude about the rate of growth of the natural logarithmic function? f(x) = ln x, g(x) = the square root of x

### Differentiation over Interval Values

1. Suppose f'(t) <0 for all t in the interval (2,8). Explain why f(3) > f(5) 2. Suppose f(0) = 3 and 2 is less than or equal to f'(x) which is less than or equal to 4 for all x in the interval [-5,5]. Determine the greatest and least possible values of f(2).

### Differentiation

Find the length and width of a rectangle that has an area of 64 square feet and a minimum perimeter.

### Differentiation - Point on a graph

Please solve and explain how to do so. Find the point on the graph of the function that is closest to the given point. f(x) = the square root of x Point: (4,0)

### Differentiation and chemical reaction

Please solve to the specified answer and explain how to do so. In an autocatalytic chemical reaction, the product formed is a catalyst for the reaction. If Q sub zero is the amount of the original substance, and x is the amount of catalyst formed, the rate of the chemical reaction is dQ/dx = kx(qsubzero - x) For what

### Inflection and concavity

Please find the points of inflection and discuss the concavity of the graph of the function. Please explain as much as possible. Please show how to obtain these answers. f(x) = x/x^2 + 1