Derivatives

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Functions : Implicit Differentiation and Rate of Change

12. Use implicit differentiation to find the slope of the curve y^2 - y + 2x = 0 at the point (x,y)=(0,1). (See attachment for full questions) 13. A spherical balloon is leaking...

Maximum/Minimum, Growth Rate, Derivatives and Chain Rule

Find the absolute maximum and minimum of f(x)= x^3 - 3x for -1<=x<=3. (See attachment for full questions)

Implicit Differentiation Product Rule

X^2-2xy+y^3=5 find dy/dx using implicit differentiation using product rule

Derivatives : First Principles and Leibniz Notation (Five Problems)

Please assist me with the attached problems, relating to first principles and Leibniz Notation.

How to Find the Derivative?

Find the derivative of the following function: x^2y^2=1 Make sure to show all work required.

Find the Derivatives of the following function

Find the derivatives of the following function: Y=(1/sin^2 x)-(2/sin x)

Chain Rule Differentiation

Please See Attachment. Suppose f: R  R is differentiable and let Show that

Directional Differentiation

Let (see equation in attached file). - find all the directional derivatives of f at 0 - is f continuous at 0? - Is f differentiable at 0?

Mathematics/derivatives and curve sketching

Find the derivative of f(x)= (3-4x^2)/(x^2-x-6) and then determine intervals of increase/decrease,local max and min values and points of concavity and inflection. Also, please tell me that if the derivative of the function is (4x^2+42x+3)/(x^2-x-6) then do I use the denominator or numerator to determine whether the function is

Derivatives & Points of Concavity of Inflection

Find the derivative of f(x)= (3-4x^2)/(x^2-x-6) and then determine intervals of increase/decrease,local max and min values and points of concavity or inflection.

Gompertz Equation

2. The Gompertz equation y'(t) = y[a-b*ln(y)] is an important model for avascular tumor growth. In the avascular growth phase, tumor cells obtain nutrients directly from the surrounding tissue. (The transition from avascular to vascular growth is marked by the onset of angiogenesis, the formation of blood vessels, which are

Derivatives and Rate of Change : Calculate the rate a shadow is moving up a wall.

I need to determine how fast a shadow is moving up a wall. Given the heigth of the wall the height if the object that cast the shadow. The length of the wire the object moves on, and the height of the light that casts the shadow. I have worked out the first sections in an Excel 2000 spreadsheet but I need a push in the right di

Motion stability and small oscillations

The morse potential is D*[1-exp(-ax)]^2 , where D, a are positive constants. Show that x=0 is a stable equilibrium, and that the period of small oscillations about it is... (See attachment for full question)

Lagrangian multipliers

1) Who can explain me Lagrangian multipliers with drawings scheme etc... 1)I just can't imagine what is happening in space with Lagrangian multipliers. 2) I did this problem but here also I can't understand it, because I can't understand what is happening in space! could you explain it with drawings and schemes please : the

Method of Partial Differentiation Question

When I write (Wx)y it means the partial derivative of W according to x with y constant ! Supposethat g(x,y)=c a constant and W=f(x,y,z) . Which of the following makes sense as the derivative Wx ? : a) (Wx)x b) (Wx)y c) (Wx)z 2) suppose that cos(x-y)=5u and W=x^2*y*u. Find (Wu)x. 3) Consider the cu

Derivative and a Tangent Line

Compute the derivative of the given function and find the equation of the line that is tangent to its graph for the specified value of x0. Equation: f(x)= x^3-x; x0=-2

Solve: Computing a Derivative

Complete the following: Solve for the derivative of the given function, finding the slope of the line that is tangent to its graph for the specified value of the independent variable f(x) = x^2-1; x=-1

Find the Gradient of the function

Find the gradient of the function: (3√θ^3) / 2sin2θ I have a number of these questions to complete could you please explain each step involved to get the correct answer

Evaluation the radius of curvature

Curvature (III) Differential Calculus Evaluate the radius of curvature at any point (x,y) for the curves : (a) xy = c2 (b) y = (1/2)a(ex/a +

Derivative Functions Given

A) f(x) = -4x-1 (-4x to the -1) f'(x) =

Question about Limits and Derivatives

Please show me all of your work so that I can understand how to do the problems correctly. Please double check all of your answers to that you are sure everything is correct. Thanks. 1. Find the limit L. Then use the definition to prove that the limit is L. . 2. Find the limit: . 3. Calculate the derivative of .

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