[ap calc] d/dx [e^(x^(2) +3)]

Question

zepdrix · Answer

$$\large \frac{d}{dx}e^{(x^2+3)}$$

Recall that the derivative of $e^x$ is $e^x$.
We'll have the same thing happen here, the derivative of the exponential will give us the same thing back. But in this problem, since our exponent is more than just $x$, we'll apply the chain rule.

zepdrix · Answer

We'll apply the chain rule* Multiplying our answer by the derivative of the exponent.

zepdrix · Answer

$$\large \frac{d}{dx}e^{(x^2+3)} \qquad = \qquad e^{(x^2+3)}\frac{d}{dx}(x^2+3)$$Understand what we did there? The exponential gives us the same thing back and then we have to multiply by the derivative of the "inner function" (the exponent).
The d/dx in front is to show that we still need to differentiate that part.

anonymous · Answer

so final answer would be$$2xe ^{x ^{2}+3}$$

zepdrix · Answer

yes good job :)

anonymous · Answer

thank you :)

anonymous · Answer

okay, can you help me with one more?