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

The derivative of y=(tan(1/x))^{sec(1/x)} is

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

The first derivative of y=(tan(1/x))^{sec(1/x)} is

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derivative of

y = (tan (\frac{1}{x}))^{s e c (\frac{1}{x})}

tan^{s e c (\frac{1}{x})} (\frac{1}{x}) (- \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} ) ln ( tan ( \frac{1}{x} ) )}{x ^{2}} - \frac{sec ^{3} ( \frac{1}{x} )}{x ^{2} tan ( \frac{1}{x} )})

Solution steps

\frac{d}{d x} ((tan (\frac{1}{x}))^{s e c (\frac{1}{x})})

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (sec (\frac{1}{x}) ln (tan (\frac{1}{x}))) = - \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} ) ln ( tan ( \frac{1}{x} ) )}{x ^{2}} - \frac{sec ^{3} ( \frac{1}{x} )}{x ^{2} tan ( \frac{1}{x} )}

= e^{s e c (\frac{1}{x}) l n (t a n (\frac{1}{x}))} (- \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} ) ln ( tan ( \frac{1}{x} ) )}{x ^{2}} - \frac{sec ^{3} ( \frac{1}{x} )}{x ^{2} tan ( \frac{1}{x} )})

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

= tan^{s e c (\frac{1}{x})} (\frac{1}{x}) (- \frac{sec ( \frac{1}{x} ) tan ( \frac{1}{x} ) ln ( tan ( \frac{1}{x} ) )}{x ^{2}} - \frac{sec ^{3} ( \frac{1}{x} )}{x ^{2} tan ( \frac{1}{x} )})

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

\int \frac{3 ^{2 x}}{1 + 3 ^{2 x}} d x

x \to \infty lim (tan (\frac{7}{x}))

\frac{d}{d x} (6 x^{2} + 15 x y + 3 y^{2})

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