Write 2x+3x\displaystyle \frac{2\sqrt{x} + 3}{x}x2x+3 in the form 2xp+3xq2x^p + 3x^q2xp+3xq, where p p\,p and q q\,q are constants.
Given that y=5x−7+2x+3x,x>0\displaystyle y = 5x - 7 + \frac{2\sqrt{x} + 3}{x}, \quad x > 0y=5x−7+x2x+3,x>0, find dydx\displaystyle \frac{dy}{dx}dxdy, simplifying the coefficient of each term.
19 exam-style questions on Edexcel A Level Old Maths Differentiation and Integration 1. Each one has a worked solution and a mark scheme showing where the marks go.