347 Answered Questions for the topic Derivatives


Calculus: Rates of change (problem below)

The lower base of a trapezoid is 6 m. If its height is increasing at the rate of 1 m/sec while its area is increasing at the rate of 2 m^2/sec. At what rate is the upper base of the trapezoid... more


Calculus Question

I have created a scatter plot and the exponential function I found is y = 30e-0.004t. I need help solving the rest of the questions. A brief explanation of each part will also suffice.Codeine... more


I’m attempting to sketch the graph of the following question, how would I answer the interval chart steps below?

Info:the interval is for the following function, y = cos(2x) —————- 3-2sin2(x) I’m sketching the graph of it dy/dx can only be positive or negative slope can only be up or... more


Help! Would this be the correct answer to the following logarithmic differentiation problem?

Use logarithmic differentiation to find the derivative of the function y= (2x+5)3(5x2-2x)4 ——————— √2x+5 the answer that I got was dy/dx=... more
Derivatives Math Calculus Derivative


antiderivative question

find ∫ (3^x - 5)(4^x + 7) dx
Derivatives Calculus Optimization


How would I answer this derivative application question?

Water is leaking from a trough at the rate of 0.8 L/s. The trough has a trapezoidal cross section, where the width at the bottom is 55 cm, at the top is 85cm, and the height is 25 cm. The length of... more


How would I answer the following question?

Give an example of a situation in which a composite differentiation might be used. Give examples of functions that may be applicable and show how the relevant rates of change might be calculated.


f(x) = 2x^4-6x^2+7

 Find an equation of the line tangent to the graph of f at x=3


How would I answer this question?

Use the process of implicit differentiation to find dy/dx given that:5x3y4 + 3y2/4x3 = 5xyApply directly without first simplifying the equation.thank you.* edit: I tried answering the question but... more
Derivatives Math Calculus


Derivative question, can someone explain it to me?

Differentiate tan(x-y)= y/((x^2)-2). Do not solve for y'
Derivatives Math Calculus Precalculus



A 14-foot ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s., how fast will the end be moving away from the wall when the top is 6 ft. above the... more
Derivatives Math


Volume of circular cylinder

If the volume of the circular cylinder is given with the 𝑽=𝝅𝒓𝟐𝒉 and 𝟕𝒓=𝟓𝒉, if the height increases by 0.02 m/sec, Find the rate of increase in the volume of the cylinder when 𝒉=𝟏𝟒𝒄𝒎
Derivatives Calculus


Determine point(s) on curves where the slopes of the tangent are equal

Given:f(x)= 18x^3 - 12x^2 - 30x +1 g(x) = 16x^3 - 9x^2 - 66x +3


for these 2 questions, how do you know they are differentiable? and how do you find the expressions?

If f is a differentiable function, find an expression for the derivative of each of the following functions:a) g(x) = f(x2) for this one I got 2x but I don't understand why it is supposed to be... more
Derivatives Calculus Rates


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


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


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


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


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) =


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


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

Critical Values, Partition Numbers, and the Increasing/Decreasing Test

Let f(t)= 5t2/3+ t2/3a) Find all partition numbers of f(t) and list themb) Find all critical values of f(t) and list themc) Find the interval where f(t) is increasingd) Find the interval where f(t)... more

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