Recall Some Standard Results of Differentiation

Before working through this chapter, it helps to recall the standard derivatives and differentiation rules you've already met in Class XI. For a power function, $\dfrac{d}{dx}(x^n) = nx^{n-1}$; for an exponential function, $\dfrac{d}{dx}(a^x) = a^x \log a$ and, as a special case, $\dfrac{d}{dx}(e^x) = e^x$; and for the natural logarithm, $\dfrac{d}{dx}(\log x) = \dfrac{1}{x}$. The derivative of any constant is zero.

Alongside these, four basic rules let you differentiate combinations of functions: