What is the derivative of tan^{-2}(x) ?

The derivative of tan^{-2}(x) is -2cot^3(x)sec^2(x)

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

The first derivative of tan^{-2}(x) is -2cot^3(x)sec^2(x)

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derivative of

tan^{- 2} (x)

- 2 cot^{3} (x) sec^{2} (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

- \frac{2}{tan ^{3} ( x )} sec^{2} (x) : - 2 cot^{3} (x) sec^{2} (x)

= - 2 cot^{3} (x) sec^{2} (x)

2 t + 5

\frac{d}{d a} (\frac{( a - t ^{2} )}{( b \cdot x )})

- 12 x

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

10 x^{3}

What is the derivative of tan^{-2}(x) ?
The derivative of tan^{-2}(x) is -2cot^3(x)sec^2(x)
What is the first derivative of tan^{-2}(x) ?
The first derivative of tan^{-2}(x) is -2cot^3(x)sec^2(x)