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STEP 1: Prove that the theorem holds for n = 1. Substitute n = 1 into the equation and show that the LHS = RHS.
STEP 2: Assume that the relation is true when n = k.
STEP 3: Prove that the relat...

For any mechanics question such as this one the best way to start off is by drawing a diagram of the system and including all the forces acting on the pa...

At stationary point the derivative of y with respect to x equals zero. Find dy/dx. dy/dx = 2x - 6x^2.Set dy/dx = 0 ,giving 2x - 6x² = 0. We can rearrange this to x(1-3x) = 0 and solve...

f(x) becomes f'(x)1) First multiply out the brackets (by adding the indices) = x^4 + 2x^22) Then differentiate this. The indices moves to the front and multiplied by the number before the x. The indices i...

To simplify this equation we need to understand the rules of logarithm equations. When we add two natural logs (ln) together, we must actually multiply the contents of the brackets. For example:ln(5) + ln...