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

The derivative of x-ln(sec(x+tan(x))) is 1-sec(x)

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

The first derivative of x-ln(sec(x+tan(x))) is 1-sec(x)

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

1 - sec (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d x}{d x} = 1

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

= 1 - sec (x)

What is the derivative of x-ln(sec(x+tan(x))) ?
The derivative of x-ln(sec(x+tan(x))) is 1-sec(x)
What is the first derivative of x-ln(sec(x+tan(x))) ?
The first derivative of x-ln(sec(x+tan(x))) is 1-sec(x)