Originally Posted by

**raymac62** Hi,

I was wondering if someone could check my work for the following two short problems:

**1.** If$\displaystyle f(x)=e^{3x^2 + x}$ find $\displaystyle f'(2)$.

Solution:

Differentiate: $\displaystyle f(x)=e^{3x^2 + x}$

$\displaystyle f'(x)=(6x+1)e^{3x^2 + x}$

Substitute 2 for x.

Thus, $\displaystyle f'(2)=13e^{14}$

**2. **Find the slope of the tangent to the function: $\displaystyle f(x)=2^{x^2+3x$ when

$\displaystyle x$ is equal to 3.

Solution:

Differentiate: $\displaystyle f(x)=2^{x^2+3x}$

$\displaystyle f'(x)=2^{x^2+3x} * ln2 * 2x+3 $