Find the derivatives of the functions. g(x)=e^{3x-1}e^{x-2}e^{x}

ruigE

ruigE

Answered question

2021-06-26

Find the derivatives of the functions. g(x)=e3x1ex2ex

Answer & Explanation

2k1enyvp

2k1enyvp

Skilled2021-06-27Added 94 answers

The function we want to differentiate is
g(x)=e3x1ex2ex
Apply the exponential property
eaeb=ea+b
to get
g(x)=e3x1+x2+x=e5x3
Now we can use the generalized rule for the derivative of exponential function:
ddx(eu)=eududx
We get
g(x)=e5x3ddx(5x3)=5e5x3

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