273 Answered Questions for the topic Derivative


Trigonometric Functions

When given a trigonometric function. You are asked to find your maximum and minimum values through the first derivative. After, how would you determine the time when the maximums and minimums occur?? more


calculus for business

Derivative Math Calculus


I need help with the following derivative question.

Let f(x) = x^2 + 3x and let g(x) and its derivative g prime (x) have the values shown in the table above. If h(x) = f(g(x)) , what is h prime (2)x 1 2 3 4 5 6g(x). 0 1 3 7 2 5g’(x) 4 3 1... more


A particle moves along the x − axis so that its position, x(t) at the time t is given by x(t)=-1/2cos(-2t^3)

a). Find the acceleration of the particle at t=2b). Find the average acceleration of the particle on the time interval [1,3]Answers should be up to the 3rd decimal place in accuracy, units are not... more
Derivative Calculus


Find the first partial derivatives at a point

f(x,y)= (x-4y)/(x+4y) at the point (x,y)=(3,4).∂f/∂x(3,4)= ?∂f/∂y(3,4)=?
Derivative Calculus Lybniz


Derivatives using Lybniz notation (Reversed)

Find dy/dx​ when y=2x^2 (assuming x≥0) Find dy/dx​ when y=−x^3 Find dy/dx​ when y=8x^3
Derivative Math Calculus Physics


How can I solve this?

Consider the curve defined by y^2=x^3−3x+3 for x>0. At what value of x does the curve have a horizontal tangent?a) √3 / 3b) 1c) √3d) There is no such valueThank you
Derivative Calculus


The line y=9x+b is tangent to the graph of f(x) =ax^3 at x=1. Find the values of a and b.

The answer is a=3, and b=-6 according to the answer key. I am confused and could not find this in the book. Please help.
Derivative Calculus


Consider the curve given by the equation y^2-2x^2y=3

Consider the curve given by the equation y2-2x2y=3. a) Find dy/dx . b) Write an equation for the line tangent to the curve at the point (1, –1). c) Find the coordinates of all points on the curve... more
Derivative Math Calculus Prove


Calculus Problem Read Description

Use the logarithmic differentiation process to PROVE the “scalar multiple” rule for derivatives.
Derivative Calculus


Derivative Explanation Help

Basically, I am trying to prove that number 15 relates to the graph of D, but I was wondering if my explanation was correct. Here is the problem and here is what I wrote. Also, I was wondering if... more


I need step by step help to find the derivative of a problem, using FTC part 1 please.

g(x) =∫xx^2 (2t2 + 3) dt


Let y be defined implicitly by the equation ln(8y)=5xy.

A) Use implicit differentiation to find the second derivative of y with respect to x. ((d^2)y)/(d(x^2)= ? simplify your answer as much as possible. B) Find the point on the curve where... more

Let y be defined implicitly by the equation ln(8y)=5xy.

A) Use implicit differentiation to find the second derivative of y with respect to x. ((d^2)y)/(d(x^2)= ? Note: Your answer should only involve the variables x and y. You should simplify your... more

P=245−x50 and C(x)=46000+60x, x is the number of microwaves that can be sold at a price of p dollars and C(x) is the cost of production

Find the profit function in terms of x. P(x) = Evaluate the marginal profit function at x=1500. P′(1500) =
Derivative Calculus


Let f(x)=sqrt(5x+6)

Find f′(x). Find the domain of f′(x) in interval notation
Derivative Calculus


Find the 100th derivative of f(x)=x(e^−x)

Derivative Calculus Calc


A company wants to make and sell computers. The price function is p=−90x+1600 (x is the number of computers and p is the price) The weekly cost of production will be 9000$ with an extra 50$ per unit.

A. Find the revenue function in terms of x B. Find the cost function in terms of x using the production cost C. Find the profit function in terms of x D. Evaluate the marginal profit at x=250

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