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287 Answered Questions for the topic Derivatives


Applications of Sinusoidal Functions and Their Derivatives

A differential equation is an equation involving a function and one or more of its derivatives. Determine whether the function y=πsinθ+2πcosθ is a solution to the differential equation d^2y/dθ^2 +... more
Derivatives Calculus Area


Optimization Problems

A piece of plexiglass is in the shape of a semicircle with radius 2 m. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass. 


Derivative of a Polynomial Function

 Air is being pumped into a spherical balloon. The volume, V, in cubic centimetres, of the balloon is V=4/3πr^3, where the radius, r, is in centimetres.    a) Determine the instantaneous rate of... more
Derivatives Derivative Proof


Derivative of a Polynomial Function

Show that there is no polynomial function that has a derivative of x^-1.


Derivative of a Polynomial Function

Determine equations for the tangents to the cubic function y=2x^3 -3x^2 -11x +8 at the point where y=2.


Derivative of a Polynomial Function

Determine equations for two lines that pass through the point (1,-5) and are tangent to the graph of y=x^2-2.


f'(x) = 2(2/3)x-1/3 - (5/3)x2/3 = (4/3)x-1/3 - (5/3)x2/3 f"(x) = (4/3)(-1/3)x-4/3 - (5/3)(2/3)x-1/3 = (-4/9)x-4

how would I set the 1st and 2nd derivatives to zero and solve for x ?


f(x)=x^2/3 (2-x) = x^2/3 (2-x)

find 1st and 2nd derivative for x to the 2/3 * (2-x) =  x to the 2/3 * (2-x) sorry I didn't clarify


f(x)=x^2/3 * (2-x) = x^2/3 * (2-x)

find the 1st and 2nd derivative

inverse derivative: y=sec^-1 1/t

please answer, i dont understand how to go about this problem. 
Derivatives Calculus


Urgent! Please help me! I have an exam in two days and I really need help with these questions. Please explain the steps and answers as thoroughly as possible.

1. Find the derivative f'(x). (a) f(x)=xexcosx (b) f(x)=secxtanx (c) f(x)=sinx/1+cosx   2. Let g(x) be a differentiable function such that g(0)=2 and g'(0)=3. (a) f(x)=(g(x))3 (b)... more



f(x)= (5x2 -7)(x2-2) / x2+6 find f ' (x)  at x=5    
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