287 Answered Questions for the topic Derivatives

#### how to solve integration of (3x+5)^4

how to solve integration of (3x+5)^4

07/28/17

#### Rate of Change

An object is moving in a straight line from a fixed point. The displacement s(in meters) is given by s=-2t^2+28t+45, t is greater than or equal to 0, where t is in seconds.
1. Describe the...
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07/28/17

#### Rates of Change

An object is moving in a straight line from a fixed point. The displacement s(in metres) is given by s=-2t^2+28t+45, t is greater than or equal to 0, where t is in seconds.
Find t when the...
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07/28/17

#### Optimization

Dianna wants to enclose a rectangular flower plot that adjoins a brick retaining wall. If she has only 30 m of decorative fencing, what should be the dimensions of the flower plot be so that she a...
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07/27/17

#### Optimization

You want to produce a cylindrical water container with a capacity of 350mL. What dimensions will minimize the amount of material required for the container?

#### Calculus Question

Differentiate y = (2x+5)^3(6x-1)^5. Express your answer in factored form.

#### how do you prove that the derivative of x^n is nx^n-1

how do you prove that the derivative of x^n is nx^n-1

Derivatives

07/11/17

#### Derivative based question

If f(x) is a function such that f(x) + f''(x)=0 and g(x)= (f(x))²+(f'(x))² and g(3)= 8, then g(8)= ?

Derivatives

06/27/17

#### Given that f '(20) = 3, what is the approximate change in the revenue if Odyssey increases its advertising budget from $20,000 to $21,000?

i have tried to understand this but i cannot and my homework is due at 6 pm! Please help

05/20/17

#### Derivative/Calculus question

Calculus Question - Please helpAn object is thrown from a height H above an uneven ground described by a height function h(x). Suppose that the object can be thrown with maximum velocity v at an...
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#### What is the integral of a function: (e^(-x))cos(x/2) dx ??

The answer which I got was (e^(-x))sin(x/2)-cos(x/2)(e^(-x))
However all the math solvers on the internet are giving different answers. Could you clear things up and tell me a definite...
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04/24/17

#### Help proving differential equation

I', really stuck on this one HW question:
I have to show how dC/dt = (D * (d^2C/dx^2)) + P at steady state (so when cD/dt =0)equals: (d^2C/dz^2) + (Pa^2/D C(a)) = 0 using C= C(x)/C(a) and z=x/a...
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Derivatives

04/22/17

#### The height reached in time t by a particle thrown upward with a speed u is given by h=ut-1/2gt^2. Find the time taken in reaching the maximum height.

(Hint for h to be maximum, dh/dt=0)

Derivatives

04/02/17

#### derivitives

The length of a rectangle is given by the function l(t)=6t+5 and its height is given by the function h(t)=the sq root of t, where t is time in seconds and the dimensions are in centimeters. Find...
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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.

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.

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

#### Derivative of y= (sec5x)^((x^2)-x+2)

Just need the first derivative of this function, struggling with there to begin

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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