356 Answered Questions for the topic Derivatives

03/06/17

Find the slope of the tangent to the curve y^2=((x^2)/(xy-28)) at (8,4)
the problem is stated as above. I'm just not sure where to start. 
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03/06/17

Shortest length of a road
Two corridors 3m and 4m wide meet at right angles. Find the length of the shortest thin straight road that can pass horizontally around the corner.
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Derivatives Calculus, Derivates

02/16/17

Derivatives of Polynomials, Sum and Constant Factor Rules?
A farmer’s barn is 60 feet long on one side. He has 150 feet of fence and wishes to build two adjacent rectangular pens of equal area along that side of his barn. What should be the arrangement and... more
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Derivatives Integration

02/16/17

a(t)=3t^2 + 2t
Take the above function. If x=1, the velocity is 0 and position is -22.  FInd v(t) at any time. Find x(t) at any time.   I have no clue how to answer this. Absolutely no clue.
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Derivatives Math Calculus Volume

02/09/17

Extending Differentiation (Confused...)
VOLUME : A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is (a) 30 cm and (b) 60... more
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Derivatives Math Calculus Math Help

02/09/17

Extending Differentiation (Question)
A curve has equation y=(x2+1)4+2(x2+1)3. Show that dy/dx=4x(x2+1)2 (2x2+5) and hence show that the curve has one stationary (critical) point. State the coordinates of the stationary point and, by... more
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Derivatives Calculus 2

02/03/17

Calculus 2 Rates - Newton's Law of Cooling
(1 point) Newton's Law of Cooling states that the rate at which an object cools is proportional to the difference in temperature between the object and the surrounding medium. Thus, if an object is... more
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01/23/17

Find (f −1)'(a). f(x) = 4x^3 + 4x^2 + 3^x + 4, a = 4
 Find (f −1)'(a).  f(x) = 4x^3 + 4x^2 + 3^x + 4, a = 4
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Derivatives Math Calculus Derivative

12/07/16

Derivative of y= (sec5x)^((x^2)-x+2)
Just need the first derivative of this function, struggling with there to begin
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Derivatives

11/09/16

What is the derivative for e^(x+y) = y?
What is dy/dx for e^(x+y) =y
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Derivatives

11/09/16

Differentiate not using first principles
a)   f(x) =  3x3 - 4√x + 1     b)  f(x)  =  2x (3x2 - x)      c) f(x) =  (x2 + x - 6)  /  (x-2)
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Derivatives Functions

11/05/16

Increasing and decreasing functions
F (x)=(12x-3)e^x
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10/31/16

I need help finding the derivative for this problem using the product rule
f(x)=(4x-4)((5x^3)-(x^2)+1)
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Derivatives

10/31/16

Where did this derivative come from ?
f(x)= x^x2    I got f'(x)= x^x2 (x+2xlnx)    It says the answer is x^x2+1 (1+2lnx)    I have no clue how to get to that answer. What am i missing ? 
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Derivatives Math Calculus Trigonometry

10/27/16

Find the derivative of cos(sqrtx)^3
I am not sure how to do this. So far I did Cos(x^(1/2)^3 So I did the chain rule to make Cos(u) where u = x^(3/2) Then I got -Sin(sqrtx)^3*(3/2)x^(1/2) Which then simplifies to... more
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Derivatives

10/24/16

Chain rule for derivatives...why is my answer wrong?
y=(4-2x-3x2)5 y'= 5(-3x2 -2x+4)4*(-6x-2)   I used a online derivative calculatir to check my answer but it gave something completly different. 
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Derivatives

10/17/16

derivative of y = e^((k)tan(sqrt(3x)))
derivative of y = e^((k)tan(sqrt(3x)))
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Derivatives

10/16/16

derivative of y = [x + (x + sin(x)^2)^3]^7
derivative of y = [x + (x + sin(x)^2)^3]^7
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Derivatives

10/16/16

Use limit definition and find equation of tangent for f(t)=sqrt(3t+5) , a=—1
Hi, I tried solving this and got (1)/(2sqrt2) but my book says the answer is (3)/(2sqrt2) 
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Derivatives

10/16/16

Suppose that f(2) = -5, g(2) = 3, f '(2) = -2, and g'(2) = 1. Find h'(2) for h(x) = g(x)/(1+f(x))
Suppose that f(2) = −5, g(2) = 3, f '(2) = −2, and g'(2) = 1. Find h'(2) for h(x) = g(x)/(1+f(x))
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10/10/16

Find the side lengths x and y of the largest area where L is a given length for the diagonal. At the critical point, y=? x=? A=?
It says to eliminate one variable so I eliminated x.   A=xy L2=x2+y2 x=(L2-y2)1/2   A=y*(L2-y2)1/2     =(L2y2-y4)1/2 Derivative =1/2(L2y2-y4)-1/2 *L22y-4y3   I don't know where to go... more
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10/07/16

Find where the function is increasing and decreasing
The derivative of a polynomial is f'(x) = (x-3)^2 (x+7)
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10/07/16

How fast is the distance from the particle to the origin changing at this instant?
the particle is moving along the curve y=sqrtx. As the particle passes through the point(4,2) its x-coordinate increases at a rate of 3cm/s.  How fast is the distance from the particle to the... more
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Derivatives Math Calculus Math Help

10/06/16

Use the definiton of a derivative to solve -2x+5
So far I have: y=-2+5   y1 = (-2(x+h)+5-(2x+5))/h   (-2-2h+5-2x-5)/h   (-4x-2h)/h   If I set h=0 it becomes -4x/0 which is undefined... What am I doing wrong?    
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Derivatives Calculus F(x) Inverses

09/29/16

Derivatives of Inverse Functions
"Suppose g is the inverse function of a differentiable function f, and G(x)=1/g(x). If f(3)=7 and f'(3)=1/9, find G'(9). FInd G'(7)."   Please show all steps- thanks so much!!
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