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Whenever there is an equation in the form f(x)=u/w, the quotient rule tells us that:

   f '(x)= [w(du/dx)-u(dw/dx)]/v²  *It looks complecated but if you break it down, it is si...

First you must show that the statement on the right hand side is true for n=1:
Σ_i=0 i² when n=1, is equal to 1²=1
(1/6)(1+1)(1+2)=(1/6)(2)(3)=1
This means t...

To differentiate X^a, where a is any real number, you multiply X by a, and subtract 1 from the power.
i.e. d(X^a)/dX=aX^a-1

x² + y² + 10x + 2y - 4xy = 10

Start by differentiating both sides by x, the terms not containing y are differentiated normally, x² becomes 2x, 10x becomes ...

y = e^2x(x²+1)^5/2

The first step is to calculate dy/dx. We can do this by splitting y into two parts and using the chain rule of differentiation: