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2x/[(x+1)(2x-4)] = [A/(x+1) + B/(2x-4)]x = A(x-2) + B(x+1)x = -1-1 = A(-3)A = 1/3x = 2 2 = B(3)B = 2/3 therefore.... 2x/[(x+1)(2x-4)] ...

Let us procede by induction:

First case: n=1. Then LHS (left hand side) = 1 and RHS (right hand side) = 1(1+1)/2 = 1. Therefore, we see that the statement is true for n=1.

Now, we carry out ...

x = ln (sec (2y))

The chain rule states that d/dy f (g (y)) = f'(g(y)). g'(y)

Here g(y) = sec(2y) so g'(y) = 2.sec(2y).tan(2y)

And f(y) = ln (y) so f'(y) = 1 / y

Thus dx/dy = (...

f''(x) means that we need to differentiate the function f(x) twice (f'(x) would mean we need to do it once). Differentiation means we multiply the coefficient by the power, and subtract one from the power...

The first thing to look at is l2 and l1 being perpendicular. This means the gradients of the two lines multiplied together = -1 . To determine the gradient a student could differentiate l1 but a slightly ...