Differentiate f(x)=(x+sin(2x))^4

This is an actual question from an EdExcel C3 paper worth 4 marks. Ok so first thing we do is look at the function and try and determine which of our 3 differentiation rules we use. Is it a Product / Quotient / Composite function? Well it isn’t in the form y=f(x)g(x) nor the form y=f(x)/g(x) so it cannot be a product or quotient. As the function is written as y=f(x)^n we can use a method to differentiate a composite, ie, the chain rule! We recall that the chain rule to differentiate y=f(x)=g(x)^n is given as f’(x)=n (g(x)^n-1) * (g’(x)). So we look back and see our n=4. Before we whack it all in the formula we look at g(x)=x+sin(2x), and differentiate this, g’(x)=1+2cos(2x); now were home and dry. All that’s left is to stick everything into our formula and jobs done! So our answer is f’(x)=4(x+sin(2x))^3 * (1+2cos(2x)). Happy 4 marks!