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Tpy6a [65]
3 years ago
15

What is the derivative of g(x)=e^(x^2+2x)+3x

Mathematics
2 answers:
igor_vitrenko [27]3 years ago
8 0
g(x)=e^{x^2+2x}+3x\\
g'(x)=e^{x^2+2x}\cdot(2x+2)+3\\
g'(x)=2e^{x^2+2x}(x+1)+3

UNO [17]3 years ago
7 0
Ok first we can split it in two : e^{x^2+2x} and 3x.

The derivative of 3x is 3.

For the first part, we use the chain rule : [f(g(x))]'=g'(x)f'(g(x)) hence (e^{x^2+2x})'=(x^2+2x)'e^{x^2+2x} (since the derivative of the exponential is itself) hence g'(x)=(2x+2)e^{x^2+2x}+3
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