"Find the derivatives of the functions. t(x)=32x−3" was answered by our community

Tobias Ali

Answered question

2021-06-04

Find the derivatives of the functions.

t (x) = 3^{2 x - 3}

Answer & Explanation

escumantsu

Skilled2021-06-05Added 98 answers

Recall the generalized derivative rule for exponential functions:

\frac{d}{d x} [b^{u}] = b^{u} \ln b \frac{d u}{d x}

In this exercise, we want to find the derivative of

t (x) = 3^{2 x - 4}

To make use of the rule, denote the argument of the exponential function by u, i.e.
u=2x-4
Using the rule from Step 1, we get:

t^{'} (x) = 3^{u} \ln 3 \frac{d u}{d x} = 3^{2 x - 4} \ln 3 \frac{d}{d x} (2 x - 4)} = 2

2 \dot{{} 3^{2 x - 4} \ln 3

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