Q 23. - Calculus

Question

Find the derivatives of the functions: $f\left(x\right)=e^x\left(x^2+3x-1\right)$

Step-by-Step Solution

Answer

The required answer is $\left(x^2+3x-1\right)e^x+e^x\left(2x+3\right)$.

Step 1. Given information.

The given function is: $f\left(x\right)=e^x\left(x^2+3x-1\right)$

Step 2. Find the derivative of the given function.

$$\begin{gathered} f\left(x\right)=e^x\left(x^2+3x-1\right) \\ f\text{'}\left(x\right)=\frac{d}{dx}{e}^x\left(x^2+3x-1\right) \\ =\left(x^2+3x-1\right)\frac{d}{dx}{e}^x+e^x\frac{d}{dx}\left(x^2+3x-1\right) \\ =\left(x^2+3x-1\right)e^x+e^x(2x+3) \end{gathered}$$