Differentiate the following: 3/2 x^(3/4) + 1/3 x^(-1/4)

In simple differentiation, we can use the fact that if y= x^n, dy/dx is equal to nx^(n-1). In other words, multiply the x term by the power, then decrease the power by 1. Here we have 2 terms so approach them seperately- firstly multiplying the x term - 3/2 multiplied by 3/4 gives 9/8, and 3/4 take away 1 is -1/4. This means the derivative is 9/8 x^(-1/4). Approach the second part in exactly the same way: 1/3 multiplied by -1/4 gives -1/12. -1/4 take away 1 gives -5/4. Therefore the overall answer to the question is 9/8x(-1/4) - 1/12x(-5/4)