Click the backdrop or press space to generate a differential to try. Click the Level button to change the difficulty level.
This is a tool designed to help with evaluating easy derivatives using the power rule. I'm trying to teach myself calculus right now and so this is a way to teach yourself simple derivatives. The power rule states that when evaluating an eligible derivative (every derivative in this project is eligible) you do it by using the formula d/dx[nx^p]=(pn)x^(p-1). So, for example, the find the derivative of x², you can use the power rule: d/dx x² = 2(x²⁻¹) = 2x Alternatively, the formal definition of the derivative states that f'(x) = lim {h → 0} [f(x + h) - f(x)] / h. So, you can also use: d/dx lim {h → 0} x² = [f(x + h) - f(x)] / h = lim {h → 0} [(x + h)² - x²] / h = lim {h → 0} [(x + h)(x + h) - x²] / h = lim {h → 0} (x² + h² + 2hx - x²) / h = lim {h → 0} (h² + 2hx) / h = lim {h → 0} h + 2x = 0 + 2x = 2x Either way is fine, they will both get you the same answer! However, keep in mind that the power rule only works for functions in the form ax^n.
