325 Answered Questions for the topic Derivative

Derivative Math Calculus Trig


(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


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


What's the quotient rule in words?

Derivative Calculus Quotient Rule


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

Derivative Calculus Product Rule


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

Derivative Calculus Power Rule


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

Derivative Math Calculus


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


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


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


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


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


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


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) = ?


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


Derivative Equations

Derivative Calculus


Derivative Equations

Derivative Calculus Derivatives


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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