325 Answered Questions for the topic Derivative

Derivative Math Calculus Trig

5d

(Falling ladder question); A ladder 25 ft long is leaning against a wall. The base of the ladder is pulled away from wall at rate of 2ft/sec.

A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second.(a) What is the velocity of the top of the ladder... more
Derivative Math Calculus

8d

finding population, with derivatives.

A population of 460 bacteria is introduced into a culture and grows in number according to the equation below, where t is measured in hours. Find the rate at which the population is growing... more

Let f(x) = 1/(1-x). Find a cubic polynomial p(x) so that f(0) = p(0), f'(0)=p'(0), f"(0)=p"(0), f'''(0)=p'''(0)

Please show working...Consider if f were a more complicated function. How would this be more efficient to finding values of f?Thank you!!
Derivative Calculus Quotient Rule

06/23/21

What's the quotient rule in words?

Derivative Calculus Quotient Rule

06/23/21

Differentiate (12u^8)/(4u^4) with respect to u.

Derivative Calculus Product Rule

06/22/21

Differentiate (v^3+5v^2)(2v^7-6v^5) with respect to v.

Derivative Calculus Power Rule

06/22/21

Differentiate 2c to the fifteenth power with respect to c.

Derivative Math Calculus

06/19/21

Question related to the mean value theorem and increasing and decreasing functions

Let L be a differentiable function on (0, ∞) such that L'(x)=1/x and L(1) = 0. Prove that for any two positive numbers a and b, L(ab) = L(a) + L(b). HINT: Begin by showing that, for any x > 0,... more

Limits, Derivative, Slope of Tangent and Equation of Tangent of a function

Consider the function f(x)= 1÷ x+3 Use the limit definition of the derivative to find the derivative of the function. Find the slope of the tangent to f(x) at x=0 Find the equation of the tangent... more
Derivative Calculus Tangent Line

06/17/21

Find the equation of the tangent line

Find the equation of the tangent line to the graph of the equation at the given point:ln(10 - y2) + 16 = -2x3 at (-2, 3)
Derivative Calculus Mathematics

06/08/21

On a given interval, if the antiderivative of f exists, is it unique? Why or why not? (You may cite theorems to support your answer.)

The question basically asks for a specific given interval, if the antiderivative of f exists, is it unique?If yes, why?If no, why not?In stating the reasons you can use specific theorems that would... more
Derivative Calculus Mathematics

06/07/21

Refer to the description below. Are there any other anti-derivatives of f(x) = 12x^2 + 2x, and g(x) = cos x. (Cite another anti-derivative for each function.)

There are already two known antiderivatives of each function, specifically:1.) f(x) = 12x^2 + 2x:Antiderivatives:4x3+x24x3+x2-12.) g(x)=cos xAntiderivatives:sin xsin x+πNow, what are the other... more
Derivative Math Calculus

06/07/21

Calculus Problem

The demand for thousands of "Zombie Death Bats" (patent pending) is given by D(p) = 124*exp(-0.0023*p), where p is the price in dollars.At what price should the "Zombie Death Bats" be sold to... more
Derivative Calculus

05/25/21

Need help with a Calculus question.

For what value(s) of x does the graph of the function f(x)=x+2 cos x have a horizontal tangent line? Justify your answer analytically (that is, without the use of graphing software)
Derivative Math Calculus

05/17/21

Let f(4) = 3 and f'(4) = 2. If g(x) = ( x f(x^2) ) / (x^2 + 1), then g'(2) = ?

https://imgur.com/a/f3j9HkBLet f(4) = 3 and f'(4) = 2. If g(x) = ( x f(x2) ) / (x2 + 1), then g'(2) = ?

05/10/21

How do I solve this Derivation Proof in Logic ¬A → [(B ∧ A) → C]?

I have attempted to solve this question multiple times but keep getting it wrong. Im only allowed to use Conjunction Introduction/Elimination, Conditional Introduction/Elimination, Negation... more
Derivative Calculus

05/06/21

Derivative Equations

Derivative Calculus

05/06/21

Derivative Equations

Derivative Calculus Derivatives

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.

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