172 Answered Questions for the topic Differentiation


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


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... more


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... more


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... more


Suppose h = f∘g. Find h'(0)

Given that f(0) = 5 f '(5) = -7 g(0) = 5 g '(0) = 4  


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.... more


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) =... more


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) =... more


Implicit Differentiation

x2y2 +y+1=0 


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... more



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!


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... more



 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... more


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.... more


differentiate w.r.t 'x'

Cos(logx + ex)


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.


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... more


Differentiate the function

g(x) = x2(1 − 8x)


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... more


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


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.


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... more


HOW DERIVE THE Differentiation of a simple power FORMULA

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