What is the derivative of ln(tan(7x)) ?

The derivative of ln(tan(7x)) is 7sec^2(7x)cot(7x)

What is the first derivative of ln(tan(7x)) ?

The first derivative of ln(tan(7x)) is 7sec^2(7x)cot(7x)

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\frac{d}{d x} (ln (tan (7 x)))

7 sec^{2} (7 x) cot (7 x)

Solution steps

\frac{d}{d x} (ln (tan (7 x)))

Apply the chain rule:

\frac{1}{tan ( 7 x )} \frac{d}{d x} (tan (7 x))

= \frac{1}{tan ( 7 x )} \frac{d}{d x} (tan (7 x))

\frac{d}{d x} (tan (7 x)) = sec^{2} (7 x) \cdot 7

= \frac{1}{tan ( 7 x )} sec^{2} (7 x) \cdot 7

Simplify

\frac{1}{tan ( 7 x )} sec^{2} (7 x) \cdot 7 : 7 sec^{2} (7 x) cot (7 x)

= 7 sec^{2} (7 x) cot (7 x)

What is the derivative of ln(tan(7x)) ?
The derivative of ln(tan(7x)) is 7sec^2(7x)cot(7x)
What is the first derivative of ln(tan(7x)) ?
The first derivative of ln(tan(7x)) is 7sec^2(7x)cot(7x)