Get the solution to "Find the derivatives of the functions. r(x)=(e2x−1)2" - Plainmath

naivlingr

Answered question

2021-06-24

Find the derivatives of the functions.

r (x) = {(e^{2 x - 1})}^{2}

Answer & Explanation

Obiajulu

Skilled2021-06-25Added 98 answers

Using the chain rule, we get

r^{'} (x) = 2 e^{2 x - 1} {(e^{2 x - 1})}^{'}

Recall the generalized rule for the derivative of exponential function:

\frac{d}{d x} [e^{u}] = e^{u} \frac{d u}{d x}

Now we get

{(e^{2 x - 1})}^{'} = e^{2 x - 1} \frac{d}{d x} (2 x - 1) = 2 e^{2 x - 1}

Substituting back, we get

r^{'} (x) = 2 e^{2 x - 1} 2 e^{2 x - 1} = 4 {(e^{2 x - 1})}^{2}

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