What is the derivative of tan^{1/x}(x) ?

The derivative of tan^{1/x}(x) is tan^{1/x}(x)(-(ln(tan(x))}{x^2}+\frac{2csc(2x))/x)

What is the first derivative of tan^{1/x}(x) ?

The first derivative of tan^{1/x}(x) is tan^{1/x}(x)(-(ln(tan(x))}{x^2}+\frac{2csc(2x))/x)

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Popular >

\frac{d}{d x} (tan^{\frac{1}{x}} (x))

tan^{\frac{1}{x}} (x) (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

Solution steps

\frac{d}{d x} (tan^{\frac{1}{x}} (x))

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

= e^{\frac{1}{x} l n (t a n (x))} (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

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

= tan^{\frac{1}{x}} (x) (- \frac{ln ( tan ( x ) )}{x ^{2}} + \frac{2 csc ( 2 x )}{x})

(u^{- 2} + u^{- 3}) (u^{5} - 9 u^{2})

\int - 3 ln (x^{2} - 1) d x

\frac{d}{d x} (ln (cos (x^{2})))

\int sin^{2} (\frac{π x}{6}) d x

x \to 1 + lim (x^{\frac{2}{1 - x}})

What is the derivative of tan^{1/x}(x) ?
The derivative of tan^{1/x}(x) is tan^{1/x}(x)(-(ln(tan(x))}{x^2}+\frac{2csc(2x))/x)
What is the first derivative of tan^{1/x}(x) ?
The first derivative of tan^{1/x}(x) is tan^{1/x}(x)(-(ln(tan(x))}{x^2}+\frac{2csc(2x))/x)