347 Answered Questions for the topic Derivatives

Derivatives Calculus

05/28/22

#### A particle moves along a straight line with equation of motions =13 - 2t. Find the smallest value of its velocity (for t ≥ 0)

Derivatives Calculus

05/28/22

#### find the location of the object traveling with a position function of s(t)=100-20t+5t^2 feet at t sec when the velocity is zero

05/28/22

#### 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...
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05/10/22

#### 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...
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05/01/22

#### 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...
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04/18/22

#### 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=...
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04/12/22

#### 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...
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04/01/22

#### 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.

Derivatives

03/30/22

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

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

03/29/22

#### 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...
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#### Derivative question, can someone explain it to me?

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

03/15/22

#### APPLICATION OF DERIVATIVES - RELATED RATES

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...
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Derivatives Math

03/10/22

#### 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

03/08/22

#### 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

03/01/22

#### 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...
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#### 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...
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#### 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...
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#### 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

09/30/21

#### 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...
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#### 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'=...
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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...
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06/18/21

#### 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)...
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