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

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

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

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

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

sec (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= sec (x)

\frac{d}{d x} (lo g_{10} (i) cos (x))

x \to - 7 lim (\frac{2}{x ^{2} ( x + 7 )})

2 y^{2} + 3 x y + (2 x y + x^{2}) y^{^{'}} = 0

\int x \cdot cos (x^{2}) d x

y^{^{''}} + 5 y^{^{'}} = 0, y (0) = 0

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