Differentiate the following equation with respect to x; sinx + 3x^2 - 2.

The first step with any differentiation question is to identify which variable you are differentiating with respect to. In this case the variable is x, so we know we're looking to differentiate each term involving the variable x. After that the simplest way to handle this kind of question is to take it term by term. The first term is a trig. function, sine. For the trig terms, the derivations can be quite complicated, however there's a few handy shortcuts that you can remember that will simplify things, for example: if you write the following list vertically down your page in this order, sine, cosine, - sine, - cosine, then we follow the list Down for Differentiation, and go up the Incline of Integration. By following this rule we see that the first term becomes cosx. Moving onto the second term we find an example of standard differentiation. This is when the variable is a part of the base of the term i.e. not part of the power/indices. For this term I personally find it helpful to visualise moving the numbers around. First we bring the power down to the front and multiply, giving us 6x^2, then we subtract 1 from the power giving us 6x^1, which is simply 6x. For the final term we can see that there are no x terms and differentiating a number will always give us zero, giving us our final answer of cosx + 6x.