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Popular >

derivative of ln(sec(x)+tan(x))

Solution

derivative of

ln (sec (x) + tan (x))

Solution

sec (x)

Solution steps

\frac{d}{d x} (ln (sec (x) + tan (x)))

Apply the chain rule:

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

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

\frac{d}{d x} (sec (x) + tan (x)) = - \frac{1}{- 1 + sin ( x )}

= \frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )})

Simplify

\frac{1}{sec ( x ) + tan ( x )} (- \frac{1}{- 1 + sin ( x )}) : sec (x)

= sec (x)

Popular Examples

derivative of x^{1/n}

\frac{d}{d x} (x^{\frac{1}{n}})

x+ye^{y/x}dx-xe^{y/x}dy=0

x + y e^{\frac{y}{x}} d x - x e^{\frac{y}{x}} d y = 0

(\partial)/(\partial u)(au)

\frac{\partial}{\partial u} (a u)

integral of x/(e^{x^2-8)}

\int \frac{x}{e ^{x^{2} - 8}} d x

(\partial)/(\partial x)(2ze^{xyz})

\frac{\partial}{\partial x} (2 z e^{x yz})

Frequently Asked Questions (FAQ)

What is the derivative of ln(sec(x)+tan(x)) ?
The derivative of ln(sec(x)+tan(x)) is sec(x)
What is the first derivative of ln(sec(x)+tan(x)) ?
The first derivative of ln(sec(x)+tan(x)) is sec(x)