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Popular >

derivative of y=x^{(1/(ln(x)))}

Solution

derivative of

y = x^{(\frac{1}{l n ( x )})}

Solution

0

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{1}{ln ( x )} ln (x)) = 0

= e^{\frac{1}{l n ( x )} l n (x)} \cdot 0

Simplify

e^{\frac{1}{l n ( x )} l n (x)} \cdot 0 : 0

= 0

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x \to 0 lim (\frac{7}{cos ( x )})

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Frequently Asked Questions (FAQ)

What is the derivative of y=x^{(1/(ln(x)))} ?
The derivative of y=x^{(1/(ln(x)))} is 0
What is the first derivative of y=x^{(1/(ln(x)))} ?
The first derivative of y=x^{(1/(ln(x)))} is 0