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

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

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

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

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

sec (x)

Solution steps

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

Treat

C

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d C}{d x} = 0

= sec (x) + 0

Simplify

= sec (x)

(9 x^{2} + 6)^{6}

\int \frac{7 sec ^{2} ( 2 x )}{3 - 5 tan ( 2 x )} d x

\frac{d}{d x} (\frac{2}{1 - 7 x})

n = 0 \sum \infty \frac{1}{n + 5}

\int \frac{x ^{2}}{( 64 - x ^{2} ) ^{\frac{3}{2}}} d x

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