Differentiation from the first principle

Question

Find the derivative of sinx-x^2

Answer 1

\(\frac{d}{dx}(sinx-x^2)\) = \(\frac{d}{dx}(sinx)-\frac{d}{dx}(x^2)\)

                        = \(cosx - 2x^(2-1)\)

                        = \(cosx - 2x^1\)

                        = cosx - 2x

Note: \(\frac{d}{dx}(sinx) = cosx \) \(\frac{d}{dx}(x^n) = n.x^(n-1)\)

Answer 2

\(f(x) = sin x - x^2\)

It's derivative is f'(x) = cosx - 2x.