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Popular >

derivative of (tan(x)^{-1})

Solution

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

Solution

- csc^{2} (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= - csc^{2} (x)

Popular Examples

integral of sec^2(x)tan^4(x)

\int sec^{2} (x) tan^{4} (x) d x

limit as x approaches infinity of e^{(-x)/(100)}

x \to \infty lim (e^{\frac{- x}{100}})

limit as x approaches-2 of (x+3)/(x+2)

x \to - 2 lim (\frac{x + 3}{x + 2})

tangent of (2x^2+2)^3(x^2-1)^2 tangent of

(2 x^{2} + 2)^{3} (x^{2} - 1)^{2}

limit as x approaches 1-of 1/(x^3-1)

x \to 1 - lim (\frac{1}{x ^{3} - 1})

Frequently Asked Questions (FAQ)

What is the derivative of (tan(x)^{-1}) ?
The derivative of (tan(x)^{-1}) is -csc^2(x)
What is the first derivative of (tan(x)^{-1}) ?
The first derivative of (tan(x)^{-1}) is -csc^2(x)