Search over 10,000 free study notes

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:

Recall that for two lines to be skew they must satisfy two conditions:

1) They must not be parallel.

2) They must not intersect.

We shall check each condition ...

The first step to solving this problem is to treat it as a normal quadratic equation; if you are struggling with comparing our equation to a normal quadratic, try substituting sin(x) = y into the equat...