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

The derivative of ln(tan^2(x)) is 2sec^2(x)cot(x)

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

The first derivative of ln(tan^2(x)) is 2sec^2(x)cot(x)

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derivative of

ln (tan^{2} (x))

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{tan ^{2} ( x )} \cdot 2 tan (x) sec^{2} (x) : 2 sec^{2} (x) cot (x)

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

y = x, y = x^{2} - 2, y = 0

x y^{^{'}} - 2 y = x^{4}

n = 0 \sum \infty e^{(2 n - 1)}

\int \frac{2 x + 1}{x ^{2} - x + 3} d x

x \to 2 lim (\frac{8}{x})

What is the derivative of ln(tan^2(x)) ?
The derivative of ln(tan^2(x)) is 2sec^2(x)cot(x)
What is the first derivative of ln(tan^2(x)) ?
The first derivative of ln(tan^2(x)) is 2sec^2(x)cot(x)