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

The derivative of ln(sec(x^2)) is 2xtan(x^2)

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

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

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

2 x tan (x^{2})

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 2 x tan (x^{2})

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\int_{- 2}^{4} x^{2} (x^{3} + 8)^{2} d x

\int y 10 + 10 y - 25 y^{2} d y

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

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