How do you find the derivative of $2e^(x+3)$ ?

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Answer 1 · 2017-01-17T01:55:13

$f(x)=2e^(x+3) => f'(x)=2e^(x+3)$

First remember a derivative times a constant equals a constant times a derivative

$(cf(x))'=cf'(x)$ in this case $c=2$

So

$(2e^(x+3))'=2(e^(x+3))'$

Then we use the chain rule $(f(g(x))'=f'(g(x)g'(x)$

$2(e^(x+3))'=2(e^(x+3))'(x+3)'$

Since $(e^x)'=e^x$

$2(e^(x+3))'(x+3)'=2(e^(x+3))(x+3)'$

Since $(f(x)+g(x))'=f'(x)+g'(x)$

$2(e^(x+3))(x+3)'=2(e^(x+3))((x)'+(3)')$

Since 3 is a constant its derivative is zero

$2(e^(x+3))((x)'+(3)')=2(e^(x+3))((x)'+0)=2(e^(x+3))(x)'$

and since $(f(x)=x => f'(x)=1$ )

$2(e^(x+3))(x)'=2(e^(x+3))(1)=underline(2(e^(x+3)))$

How do you find the derivative of 2e^(x+3) 2e^(x+3)?