What is the derivative of tan^2(sqrt(x)) ?

The derivative of tan^2(sqrt(x)) is (sec^2(sqrt(x))tan(sqrt(x)))/(sqrt(x))

What is the first derivative of tan^2(sqrt(x)) ?

The first derivative of tan^2(sqrt(x)) is (sec^2(sqrt(x))tan(sqrt(x)))/(sqrt(x))

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

x \to 0 lim (e^{4 x + 2})

f (x) = (1 + tan (2 x))^{3}

sin (- 5 x)

\int \frac{1}{cos ( u ) + 1} d u

\frac{d y}{d x} = 6 x 8 y + 17

What is the derivative of tan^2(sqrt(x)) ?
The derivative of tan^2(sqrt(x)) is (sec^2(sqrt(x))tan(sqrt(x)))/(sqrt(x))
What is the first derivative of tan^2(sqrt(x)) ?
The first derivative of tan^2(sqrt(x)) is (sec^2(sqrt(x))tan(sqrt(x)))/(sqrt(x))