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Popular >

derivative of f(x)=tan(1/x)

Solution

derivative of

f (x) = tan (\frac{1}{x})

Solution

- \frac{sec ^{2} ( \frac{1}{x} )}{x ^{2}}

Solution steps

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

Apply the chain rule:

sec^{2} (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

= sec^{2} (\frac{1}{x}) \frac{d}{d x} (\frac{1}{x})

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

= sec^{2} (\frac{1}{x}) (- \frac{1}{x ^{2}})

Simplify

sec^{2} (\frac{1}{x}) (- \frac{1}{x ^{2}}) : - \frac{sec ^{2} ( \frac{1}{x} )}{x ^{2}}

= - \frac{sec ^{2} ( \frac{1}{x} )}{x ^{2}}

Popular Examples

derivative of (100x/(x+y))=0

\frac{d}{d x} (\frac{100 x}{x + y}) = 0

limit as x approaches 5+of x/(x-5)

x \to 5 + lim (\frac{x}{x - 5})

integral from 3 to 5 of 1/(x^2-1)

\int_{3}^{5} \frac{1}{x ^{2} - 1} d x

area y=x^2,y=-2x^2+12 area

y = x^{2}, y = - 2 x^{2} + 12

integral from ln(1) to ln(2) of e^{3x}

\int_{l n (1)}^{l n (2)} e^{3 x} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=tan(1/x) ?
The derivative of f(x)=tan(1/x) is -(sec^2(1/x))/(x^2)
What is the first derivative of f(x)=tan(1/x) ?
The first derivative of f(x)=tan(1/x) is -(sec^2(1/x))/(x^2)