Question

Differentiate the Function

Answer 1

\[y=e ^{x+3}+9\]

Answer 2

\[
y=e ^{x+3}+9 \\
\frac{dy}{dx} = e^{x+2} * \frac{d}{dx}(x+2) + 0 = e^{x+2}
\]

Answer 3

\[
\frac{d}{dx}e^{x+2} = e^{x+2}* \frac{d}{dx}(x+2) = e^{x+2}
\]

Answer 4

so \[e ^{x+2}\] stays the same because of the exponent rules

Answer 5

The derivative of e^x = e^x
The derivative of e^{something} = e^{something} * derivative of {something}
(by chain rule).

Answer 6

okay thank you!

Answer 7

you are welcome.