What is the derivative of y=ln|sec(x)+tan(x)| ?

The derivative of y=ln|sec(x)+tan(x)| is sec(x)

What is the first derivative of y=ln|sec(x)+tan(x)| ?

The first derivative of y=ln|sec(x)+tan(x)| is sec(x)

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derivative of

y = ln ∣ sec (x) + tan (x) ∣

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{sec ( x ) + tan ( x )}{∣ sec ( x ) + tan ( x ) ∣ ( - 1 + sin ( x ) )}

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

Simplify

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

= sec (x)

\frac{d}{d x} (\frac{4 sin ( x )}{3 + cos ( x )})

\frac{\partial}{\partial x} (x e^{- z})

\frac{\partial}{\partial x} (x^{2} ln (y))

\frac{( 3 s + 3 )}{( s ^{2} ( s + 2 ) ^{3} )}

\frac{d P}{d t} + P = 10

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