172 Answered Questions for the topic Differentiation

10/15/19

#### Rules for Differentiation (Highschool Calculus)

Find the values of a and b so that g(x) is both continuous and differentiable at x=0.g(x){ ax+b, x > 0 1-x+x2, x (< and/or =) 0

04/29/19

#### At what rate is the water level rising?

A swimming pool is 20 m long, 5 meters wide, has sides in the shape of a right triangle, and slopes downward so that it is 4 meters deep at the deep end. Water is being pumped into the pool at 2m^3...
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04/28/19

#### Help Solving Calculus Problem

An apple farm yields an average of 39 bushels of apples per tree when 21 trees are planted on an acre of ground. Each time 1 more tree is planted per acre, the yield decreases by 1 bushel (bu) per...
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11/27/18

#### Theory of partial differentiation

WHY A TOTAL DIFFERENTIATION CAN BE RECIPROCAL BUT PARTIAL DIFFERENTIATION CANNOT BE RECIPROCALed?EX if (dx/dy)=sinp then (dy/dx)=cosecp BUT in case of partial differentiation...
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08/10/18

#### Differentiation - Chain Rule

A cone-shaped container with a hole at its top vertex is filled with water. The cone has a 4cm radius and 16cm in height. The cone was turned upside down to the let its water flow out of container....
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08/08/18

#### Differentiation - are these answers correct?

Could someone help me check if I differentiated these these two functions correctly:
f(x)= √(3x2-x3)
And
h(x) = 3√(5x+x2)2
I got: f′(x) = 6x-3x2/2·√(3x2-x3)
And
h′(x) =...
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07/24/18

#### Derivatives - local extremes

f(x) = x3 - 8x2 + 5x
Compute algebraically the x-coordinates of the points on the graph of f where the tangent to this graph is horizontal.
I know how to find the derivative:
f′(x) =...
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07/18/18

#### Differentiation - Help for exam prep!

Differentiate the following function and simplify.
h(x) = x2 · √8-x
Answer = 2x√8-x - x/2√8-x
Could you show me the step by step process and which rules to use in order to...
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07/14/18

#### Differentiation

y= -x5(1 - x)
I have to use the product rule to answer this question.
The answer is 6x5 - 5x4
Can someone explain this to me and show how to solve it?
Thank you so much!

07/10/18

#### Help with differentiation - Determine coordinates of local extreme

Need help with a question on differentiation.
*Determine the exact coordinates of the local extreme(s) of the following function. Also indicate whether it concerns a local minimum or a local...
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07/07/18

#### differentiation

b) For the curve 𝑦=𝑥𝑒^−𝑥^2 ,𝑥 ≥0 i. Find the coordinates of the point where the gradient is 0 giving your answers exactly.ii. Show that the line 𝑦=𝑥 is a tangent to the curve 𝑦=𝑥𝑒−𝑥2 and give the...
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07/06/18

#### Help regarding optimization problem

In order to construct a box whose base length is 3 times the base width with volume of 50 ft^3, using materials to build the top and bottom that cost $ 10 per ft^2 and $ 6 per ft^2 for the sides....
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06/10/18

#### Proving continuity of a differentiable function.

Hi
I have been given a function f:(a,b)→R, which is differentiable on (a,b). How do I use this information to prove that f is also continuous on (a,b)?
Thanks.

05/13/18

#### A curve is defined for x>0. the gradient of the curve at the point (x,y) is given by dy/dx = x^3/2 - 2x

I need help with part C as i am unsure what value i should put into x to find the +C
part a + b + c: a) show that there is a single value of x for which the curve has a stationary point b)find...
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05/03/18

#### Find two positive numbers that sum to 4 and such that the sum of the cube of the first and the square of the second is as small as possible

Calculus, Differentiation

04/23/18

#### How to find the angular velocity for a system after 12 seconds and report in rad/s

A system in a lab is tested under two different conditions. The angular acceleration of the system s described by the equations: a(t)=d^2const/dt^2=10cos (5t).
Find the angular velocity of the...
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04/21/18

#### Find the angular velocity of the system after 12 seconds

The angular acceleration of a system is described by the following equation: a(t)=d^2Radians/dt^2=10cos (5t).
Find the angular velocity of the system in radians after 14 seconds

04/02/18

#### Find the stationary points and stationary values of the function :- F(x) = x^3 - 3x^2 - 9x + 5.

F(x) = x^3 - 3x^2 - 9x + 5.

03/11/18

#### A car leaves an intersection traveling west. Its position 4 sec later is 22 ft from the intersection. At the same time, another car leaves the same intersection

A car leaves an intersection traveling west. Its position 4 sec later is 22 ft from the intersection. At the same time, another car leaves the same intersection heading north so that its position 4...
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