Question

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

Answer 1

\[\large \frac{d}{dx}e^{(x^2+3)}\]

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.

Answer 2

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

Answer 3

\[\large \frac{d}{dx}e^{(x^2+3)} \qquad = \qquad e^{(x^2+3)}\frac{d}{dx}(x^2+3)\]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.

Answer 4

so final answer would be\[2xe ^{x ^{2}+3}\]

Answer 5

yes good job :)

Answer 6

thank you :)

Answer 7

okay, can you help me with one more?