What is the derivative of ln(xsec(x)) ?

The derivative of ln(xsec(x)) is (sec(x))/x+sec(x)tan(x)ln(x)

What is the first derivative of ln(xsec(x)) ?

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = ln (x), g = sec (x)

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

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

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

\frac{1}{x} sec (x) = \frac{sec ( x )}{x}

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

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