432 Answered Questions for the topic Derivative

03/08/21

If f(x) = integral 3 to x^2 t^4 dt, then f'(x) =?
f(x) = ∫3x^2 t4 dt, then what is f ' (x)= ?
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03/01/21

How do you solve this pesky related rates problem? (Daily Supply)
Hi. I am stuck trying to solve this problem:In a certain market, x thousand crates of apples are supplied daily. Each crate costs p dollars, and the supply equation ispx - 20p - 3x + 105 = 0.If the... more
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02/28/21

height of rect. box is 10 inches. the length inc. at rate of 2 in/sec ,width dec. at a rate 4 in/sec. whenlength is 8 inche and the width is 6 inches, find rate at which volume of box is changing.
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02/28/21

the radius of a large balloon is increasing at a rate of 2 inches per second. how fast, in cubic inches per second is the volume increasing when the radius is 10.

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02/28/21

Let f'(x)=4x^3-12x^2 a. identify where the relative max extrema of f occur. b.Find the intervals on which f is decreasing and increasing. c.find where the graph of f is concave up concave down.

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Derivative Calculus Applications

02/28/21

A dog breeder has 40 feet to use for a rectangular dog run. If she puts the run next to the garage, she only needs to use the wire for 3 sides. What dimensions will yeild maximum area

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02/25/21

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
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Derivative Math Calculus Physics

02/23/21

One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30 ◦ , with a possible error of ± 1 . 2%, what is the error and percentage error?
Use differentials to estimate the error in computing the length of the hypotenuse and what is the percentage error?
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Derivative Math Calculus Physics

02/23/21

The radius of a sphere is increasing at a rate of 5 mm/s, how fast is the surface area increasing when the diameter is 60 mm?
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02/13/21

calculus for business
USE THE FOUR-STEP PROCESS TO FIND F1(X) AND THEN FIND F1(2), F1(4), AND F1(6).F(X) = 18√x+3
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Derivative Math Calculus

01/15/21

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
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01/11/21

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
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Derivative Calculus

01/07/21

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)=?
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Derivative Calculus Lybniz

12/31/20

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
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12/18/20

Find (f^-1)(−2) if f(x) = x.sqrt(3 + x^2) and if f ^-1(x) exists.
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Derivative Math Calculus Physics

12/14/20

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
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Derivative Calculus

12/14/20

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.
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Derivative Calculus

12/13/20

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
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Derivative Math Calculus Prove

12/09/20

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

12/06/20

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
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12/06/20

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
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Derivative Calculus Tangent Line

11/27/20

ind the slope of the tangent line to the curve sqrt(8x+y)+sqrt(8xy)=12 at the point (1,8).
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11/27/20

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
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11/26/20

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
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11/26/20

Find (d^2)y/d(x^2) at the following point using implicit differentiation: sqrt(x)+sqrt(y)=1, at (1,0)
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