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

Tobias Ali

Tobias Ali

Answered question

2021-06-04

Find the derivatives of the functions. t(x)=32x3

Answer & Explanation

escumantsu

escumantsu

Skilled2021-06-05Added 98 answers

Recall the generalized derivative rule for exponential functions:
ddx[bu]=bulnbdudx
In this exercise, we want to find the derivative of
t(x)=32x4
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)=3uln3dudx=32x4ln3ddx(2x4)}=2
2{˙32x4ln3

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