What is the derivative of tan^n(x) ?

The derivative of tan^n(x) is nsec^2(x)tan^{n-1}(x)

What is the first derivative of tan^n(x) ?

The first derivative of tan^n(x) is nsec^2(x)tan^{n-1}(x)

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\frac{d}{d x} (tan^{n} (x))

n sec^{2} (x) tan^{n - 1} (x)

Solution steps

\frac{d}{d x} (tan^{n} (x))

Apply the chain rule:

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

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

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

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

Simplify

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

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\frac{d y}{d x}, - x + y - x^{3} = y^{3} + 4 x^{2}

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