Question

differentiate. f(x)=e^{x^{2}+3x} f(x)=□

Explanation:

Step1: Recall chain - rule

If $y = e^{u}$, then $y^\prime=e^{u}\cdot u^\prime$. Here $u = x^{2}+3x$.

Step2: Differentiate $u$

Differentiate $u=x^{2}+3x$ with respect to $x$. Using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$, we have $u^\prime=\frac{d}{dx}(x^{2}+3x)=2x + 3$.

Step3: Apply chain - rule

Since $f(x)=e^{x^{2}+3x}$, by the chain - rule $f^\prime(x)=e^{x^{2}+3x}\cdot(2x + 3)$.

Answer:

$(2x + 3)e^{x^{2}+3x}$