Q 21. - Calculus

Question

Find the derivatives of the functions: $f\left(x\right)=\frac{1-x}{e^x}$

Step-by-Step Solution

Answer

The required answer is  $\frac{-e^x-(1-x)e^x}{{\left(e^x\right)}^2}$.

Step 1. Given information.

The given function is: $f\left(x\right)=\frac{1-x}{e^x}$

Step 2. Find the derivative of the given function.

$$\begin{gathered} f\left(x\right)=\frac{1-x}{e^x} \\ f\text{'}\left(x\right)=\frac{d}{dx}\left(\frac{1-x}{e^x}\right) \\ =\frac{e^x{\displaystyle \frac{d}{dx}}\left(1-x\right)-\left(1-x\right){\displaystyle \frac{d}{dx}}{e}^x}{{\left(e^x\right)}^2} \\ =\frac{e^x(0-1)-(1-x)e^x}{{\left(e^x\right)}^2} \\ =\frac{-e^x-(1-x)e^x}{{\left(e^x\right)}^2} \end{gathered}$$