What is the derivative of 5^{-1/x} ?

The derivative of 5^{-1/x} is (ln(5)*5^{-1/x})/(x^2)

What is the first derivative of 5^{-1/x} ?

The first derivative of 5^{-1/x} is (ln(5)*5^{-1/x})/(x^2)

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Popular >

\frac{d}{d x} (5^{- \frac{1}{x}})

\frac{ln ( 5 ) \cdot 5 ^{- \frac{1}{x}}}{x ^{2}}

Solution steps

\frac{d}{d x} (5^{- \frac{1}{x}})

Apply exponent rule:

a^{b} = e^{b l n (a)}

5^{- \frac{1}{x}} = e^{(- \frac{1}{x}) l n (5)}

= \frac{d}{d x} (e^{(- \frac{1}{x}) l n (5)})

Apply the chain rule:

e^{(- \frac{1}{x}) l n (5)} \frac{d}{d x} ((- \frac{1}{x}) ln (5))

= e^{(- \frac{1}{x}) l n (5)} \frac{d}{d x} ((- \frac{1}{x}) ln (5))

\frac{d}{d x} ((- \frac{1}{x}) ln (5)) = \frac{ln ( 5 )}{x ^{2}}

= e^{(- \frac{1}{x}) l n (5)} \frac{ln ( 5 )}{x ^{2}}

Simplify

e^{(- \frac{1}{x}) l n (5)} \frac{ln ( 5 )}{x ^{2}} : \frac{ln ( 5 ) \cdot 5 ^{- \frac{1}{x}}}{x ^{2}}

= \frac{ln ( 5 ) \cdot 5 ^{- \frac{1}{x}}}{x ^{2}}

3 x + 1

\frac{d}{d x} (6 x^{2} + 5 x^{3} y^{4} - 10 y^{5})

\int tan (3 x) sin (3 x) d x

\int (5 x + 4)^{6} d x

f (x) = (2 x + 1)^{6}

What is the derivative of 5^{-1/x} ?
The derivative of 5^{-1/x} is (ln(5)*5^{-1/x})/(x^2)
What is the first derivative of 5^{-1/x} ?
The first derivative of 5^{-1/x} is (ln(5)*5^{-1/x})/(x^2)