What is the derivative of y=tan(pi-9/x) ?

The derivative of y=tan(pi-9/x) is (9sec^2(9/x))/(x^2)

What is the first derivative of y=tan(pi-9/x) ?

The first derivative of y=tan(pi-9/x) is (9sec^2(9/x))/(x^2)

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derivative of

y = tan (π - \frac{9}{x})

\frac{9 sec ^{2} ( \frac{9}{x} )}{x ^{2}}

Solution steps

\frac{d}{d x} (tan (π - \frac{9}{x}))

Simplify

tan (π - \frac{9}{x}) : - tan (\frac{9}{x})

= \frac{d}{d x} (- tan (\frac{9}{x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (tan (\frac{9}{x}))

Apply the chain rule:

sec^{2} (\frac{9}{x}) \frac{d}{d x} (\frac{9}{x})

= sec^{2} (\frac{9}{x}) \frac{d}{d x} (\frac{9}{x})

\frac{d}{d x} (\frac{9}{x}) = - \frac{9}{x ^{2}}

= - sec^{2} (\frac{9}{x}) (- \frac{9}{x ^{2}})

Simplify

- sec^{2} (\frac{9}{x}) (- \frac{9}{x ^{2}}) : \frac{9 sec ^{2} ( \frac{9}{x} )}{x ^{2}}

= \frac{9 sec ^{2} ( \frac{9}{x} )}{x ^{2}}

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What is the derivative of y=tan(pi-9/x) ?
The derivative of y=tan(pi-9/x) is (9sec^2(9/x))/(x^2)
What is the first derivative of y=tan(pi-9/x) ?
The first derivative of y=tan(pi-9/x) is (9sec^2(9/x))/(x^2)