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Popular >

derivative of ln(1/(cos(x)))

Solution

\frac{d}{d x} (ln (\frac{1}{cos ( x )}))

Solution

tan (x)

Solution steps

\frac{d}{d x} (ln (\frac{1}{cos ( x )}))

Simplify

ln (\frac{1}{cos ( x )}) : ln (sec (x))

= \frac{d}{d x} (ln (sec (x)))

Apply the chain rule:

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

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

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

= \frac{1}{sec ( x )} sec (x) tan (x)

Simplify

\frac{1}{sec ( x )} sec (x) tan (x) : tan (x)

= tan (x)

Popular Examples

limit as x approaches a of 0/0

x \to a lim (\frac{0}{0})

integral of (x^2)/(x^6-4)

\int \frac{x ^{2}}{x ^{6} - 4} d x

(\partial)/(\partial x)(xe^{sqrt(6xy)})

\frac{\partial}{\partial x} (x e^{6 x y})

integral from 0 to infinity of 2/(x^2+4)

\int_{0}^{\infty} \frac{2}{x ^{2} + 4} d x

(1+x^2)(dy)/(dx)+3xy=5x

(1 + x^{2}) \frac{d y}{d x} + 3 x y = 5 x

Frequently Asked Questions (FAQ)

What is the derivative of ln(1/(cos(x))) ?
The derivative of ln(1/(cos(x))) is tan(x)
What is the first derivative of ln(1/(cos(x))) ?
The first derivative of ln(1/(cos(x))) is tan(x)