Quotient rule (Calculus)

The quotient rule states that given a function $f(x)$ in the form $\frac{u}{v}$ the derivative of the function is:

$$\frac{u^{\prime }\cdot v-v^{\prime }\cdot u}{v^2}$$

Examples#

Problem #1#

Find the derivative of $f\left(x\right)=\frac{e^x}{x-1}$.

Following the quotient rule:

$$\frac{\left(e^x\right)(x-1)-\left(e^x\right)\left(1\right)}{{(x-1)}^2}$$