What is the derivative of \sqrt[x]{2} ?

The derivative of \sqrt[x]{2} is -(ln(2)*2^{1/x})/(x^2)

What is the first derivative of \sqrt[x]{2} ?

The first derivative of \sqrt[x]{2} is -(ln(2)*2^{1/x})/(x^2)

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Popular >

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

Solution steps

Apply exponent rule:

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

= \frac{d}{d x} (e^{\frac{1}{x} l n (2)})

Apply the chain rule:

e^{\frac{1}{x} l n (2)} \frac{d}{d x} (\frac{1}{x} ln (2))

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

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

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

Simplify

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

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

\int x - x^{4} d x

n = 0 \sum \infty 2^{- 2 n}

x \to 0 lim (4^{2})

\frac{d}{d x} (\frac{36}{x})

\frac{3 s + 4}{s ^{2} - 1}

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