`y = 5^(-1/x)` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 25 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

Using the exponential function rule

`(a^(u(x)))'= ln(a)*a^(u(x))*u'(x)`

`y' = [5^(-1/x)]' = ln(5)*5^(-1/x)*d/dx(-1/x)`

`= ln(5)*5^(-1/x)*(1/x^2)`

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rommel2101 | High School Teacher | eNotes Newbie

Posted on

y=5−1/x=exp[−1/x⋅ln(5)].
Therefore,
dy/dx=exp[−1/x⋅ln(5)]⋅d/dx[−1/x⋅ln(5)](By the Exponential Chain Rule.)
=5−1/x⋅d/dx[−1/x⋅ln(5)]=5−1/x⋅1/x2⋅ln(5)
=ln(5)/5 1/x x2.

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