What is the derivative of \sqrt[3]{tan(2^{-x}}) ?

The derivative of \sqrt[3]{tan(2^{-x}}) is -(ln(2)*2^{-x}sec^2(2^{-x}))/(3tan^{2/3)(2^{-x})}

What is the first derivative of \sqrt[3]{tan(2^{-x}}) ?

The first derivative of \sqrt[3]{tan(2^{-x}}) is -(ln(2)*2^{-x}sec^2(2^{-x}))/(3tan^{2/3)(2^{-x})}

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\frac{d}{d x} (3 tan (2^{- x}))

- \frac{ln ( 2 ) \cdot 2 ^{- x} sec ^{2} ( 2 ^{- x} )}{3 tan ^{\frac{2}{3}} ( 2 ^{- x} )}

Solution steps

\frac{d}{d x} (3 tan (2^{- x}))

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{3 tan ^{\frac{2}{3}} ( 2 ^{- x} )} (- ln (2) \cdot 2^{- x} sec^{2} (2^{- x})) : - \frac{ln ( 2 ) \cdot 2 ^{- x} sec ^{2} ( 2 ^{- x} )}{3 tan ^{\frac{2}{3}} ( 2 ^{- x} )}

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

x (1 + y^{2}) d x + y (1 + x^{2}) d y = 0

x \to 0 lim (x (1))

\frac{d}{d x} (- \frac{cos ( 3 x )}{3})

\int y 1 - y^{2} d y

3 x^{- 2}

What is the derivative of \sqrt[3]{tan(2^{-x}}) ?
The derivative of \sqrt[3]{tan(2^{-x}}) is -(ln(2)*2^{-x}sec^2(2^{-x}))/(3tan^{2/3)(2^{-x})}
What is the first derivative of \sqrt[3]{tan(2^{-x}}) ?
The first derivative of \sqrt[3]{tan(2^{-x}}) is -(ln(2)*2^{-x}sec^2(2^{-x}))/(3tan^{2/3)(2^{-x})}