326 Answered Questions for the topic Derivatives

Derivatives Calculus Rates

10d

Rates question (calc1)

The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at a rate of 2 square cm/minute. At what rate is the base of the... more
Derivatives Calculus Rates

10d

Calculus rates question

A road perpendicular to a highway leads to a farmhouse located 5 mile away. An automobile traveling on the highway passes through this intersection at a speed of 50mph.How fast is the distance... more
Derivatives Calculus Area

10d

Area of a circle

Let A be the area of a circle with radius r. If dr/dt= 3 , find dA/dt when r = 1.
Derivatives Calculus

17d

Calculus (derivatives)

I am having trouble with these questions Let F (x) = f (x f (x2)). Suppose that f (4) = 6, f '(4) = 2, and f '(12) = 4. Find F '(2). Suppose that Newton's method is used to locate a root of the... more
Derivatives Math Calculus

09/11/21

Calc 1 Question

I have this question that I don't really understand since derivatives are a little confusing. (1): Find the derivative of g(t) = 5t^2 + 5t at t = 6 algebraically. g'(6) =

07/30/21

Find the rate of change of the volume for each of the radii given below if dr/dt is 5 inches per min and h=12r

The formula for the volume of a cone is given below. Find the rate of change of the volume for each of the radii given below if dr/dt is 5 inches per minute and h = 12r.V = (1/3)𝜋r2h(a) r = 8 inV'=... more

07/30/21

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.

Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.y = √x(a) Find dy/dt, given x=1 and dx/dt = 3.dy/dt = ?(b) Find dx/dt, given x=36 and... more

Use substitution to find all the antiderivatives of the function

g'(x) = 30 (ln x)9/x
Derivatives

06/11/21

Box Mini Project

Paper dimensions are 8.5 inches by 11 inches You will now have to determine the length, width, and height to make an open-top box with the maximum volume possible. To do this you will have to cut... more
Derivatives Calculus Derivative

05/04/21

Find f’(2) for f(x)= 1/x-3 using the definition of the derivative

Derivatives Calculus Derivative

05/03/21

Consider the function, f(x) = √x-4 (square root goes over x-4) at the point (8,2) find the slope of the tangent line to the curve using the definition of the derivative

And find the equation of the tangent line. I am confused on how to treat the square root as I haven’t covered a question using them like this yet.
Derivatives Calculus Optimization

03/22/21

Application of Derivatives and Optimization of Volume

Using Calculus, determine the dimensions of a rectangular solid (with a square base) with maximum volume if its surface area is 384 square centimeters. Can someone explain using derivative... more
Derivatives Calculus

02/17/21

Calculus Homework

Consider . Compute .         :               .
Derivatives Calculus

02/17/21

Calculus Homework

Consider . Compute :0  :       . 
Derivatives Calculus

02/17/21

Calculus Homework

Consider . Given , Which of the followin statements about the level curve is correct?The level curve is None of these.The level curve is      .The level curve is       .      .which of the... more
Derivatives Calculus

02/17/21

Calculus Homework

Consider  . Compute :       :    .
Derivatives Basic Calculus

01/15/21

Determine an equation of the line tangent to y=2x^2+3 that is parallel to the 8x-y+3=0.

Determine an equation of the line tangent to y=2x^2+3 that is parallel to the 8x-y+3=0.
Derivatives Math Calculus Pre Calculus

12/15/20

Calculus Challenge Question URGENT!

I need to catch my flight. I’m at the airport and I’m running late. I need to make it 1000m to get to my gate. I have two choices. I can either run or take the moving sidewalk. The moving sidewalk... more
Derivatives Calculus

12/07/20

Equation that relates the volume and height of a cone with a radius of 3

Write down an equation that relates the two quantities described. Then use implicit differentiation to obtain a relationship between the rates at which the quantities change over time. The volume V... more

11/23/20

Try and solve this: Calculus Derivative Problem...

Determine the derivative of each a & b...a.) You are given f(3) = -5, f '(3) = 6, g(3) = 4, and g'(3) = 8. Determine d/dx( f(x)/g(x) ) at x=3...b.) You are given y(9) = 4 and d/dx( ln(y) ) = -3... more
Derivatives Calculus Precalculus

11/19/20

Which of the expressions below are equivalent to u'vw +uv'w - uvw'/ w2 if u,v and w are all functions of x and a dash denotes a derivative with respect to x.

Which of the expressions below are equivalent to u'vw +uv'w - uvw'/ w2 if u,v and w are all functions of x and a dash denotes a derivative with respect to x.d/dx (uv/w)d/dx (u/vw)d/dx (1/uvw) d/dx... more
Derivatives Calculus Limits

11/19/20

Which of the following two expressions are equivalent alternatives to the definition of a derivative?

Which of the following two expressions are equivalent alternatives to the definition of a derivative?A: lim j -> 0 f(x) - f(x-j) / j B: lim j -> 0 f(x - j/2) - f(x + j/2)/ j A only B only... more
Derivatives Calculus

10/31/20

If a woman 2m tall walks from the spotlight toward the building at a speed of 0.6m/s, how fast is the length of her shadow on the building decreasing when she is 6m from the building?

The spotlight is 20 metres away. We're going through derivatives right now so so far I've tried variations of this:dx/dy = 40/((2-x)^2)@ x =640/ (14^2) - 0.6But I can't get the right answer

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