Handy Table of Integrals Power of x \begin{align*} \int a \, dx &= ax + C \\ \\ \int x^n \, dx &= \frac{x^{n+1}}{n+1} + C \qquad n \ne -1 \\ \\ \int \frac{1}{x} \, dx &= \ln |x| + C \\ \end{align*} Exponential and Logarithmic \begin{align*} \int e^x \, dx &= e^x + C… [read more]

Handy Table of Derivatives Want lots of examples to see how to calculate derivatives? Visit our free Calculating Derivatives: Problems & Solutions page! Power of x \begin{align*} \frac{d}{dx} \left(c\right) &= 0 \\[8px] \frac{d}{dx} \left(cx\right) &= c \\[8px] \frac{d}{dx} \left(cx^n\right) &= ncx^{n-1} \\[8px] \end{align*} For example, \[\dfrac{d}{dx}5x^3 = 3 \cdot 5x^2 = 15x^2 \] You’ll also… [read more]

Differentiation Rules Here’s a handy summary of the differentiation rules you’ll frequently use. Product Rule The differentiation rule for the product of two functions: \begin{align*} (fg)’&= f’g + fg’\\[8px] &= [{\small \text{ (deriv of the 1st) } \times \text{ (the 2nd) }}]\, + \,[{\small \text{ (the 1st) } \times \text{ (deriv of the 2nd)}}] \end{align*}… [read more]

Handy Table of Trig Function Derivatives Want lots of examples to see how to calculate derivatives? Visit our free Calculating Derivatives: Problems & Solutions page! \begin{align*} \frac{d}{dx}\left(\sin x\right) &= \cos x \\[8px] \dfrac{d}{dx}\left(\cos x\right) &= -\sin x \\[8px] \dfrac{d}{dx}\left(\tan x\right) &= \sec^2 x \\[8px] \frac{d}{dx}\left(\csc x\right) &= -\csc x \cot x \\[8px] \frac{d}{dx}\left(\sec x\right) &=… [read more]