"Find the derivatives of the functions. g(x)=e3x−1ex−2ex" was answered by our community

ruigE

Answered question

2021-06-26

Find the derivatives of the functions.

g (x) = e^{3 x - 1} e^{x - 2} e^{x}

Answer & Explanation

2k1enyvp

Skilled2021-06-27Added 94 answers

The function we want to differentiate is

g (x) = e^{3 x - 1} e^{x - 2} e^{x}

Apply the exponential property

e^{a} e^{b} = e^{a + b}

to get

g (x) = e^{3 x - 1 + x - 2 + x} = e^{5 x - 3}

Now we can use the generalized rule for the derivative of exponential function:

\frac{d}{d x} (e^{u}) = e^{u} \frac{d u}{d x}

We get

g^{'} (x) = e^{5 x - 3} \frac{d}{d x} (5 x - 3) = 5 e^{5 x - 3}

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