What is the derivative of ln(3x-e^{sec(x)}) ?

The derivative of ln(3x-e^{sec(x)}) is 1/x-e^{sec(x)}sec(x)tan(x)

What is the first derivative of ln(3x-e^{sec(x)}) ?

The first derivative of ln(3x-e^{sec(x)}) is 1/x-e^{sec(x)}sec(x)tan(x)

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\frac{d}{d x} (ln (3 x) - e^{s e c (x)})

\frac{1}{x} - e^{s e c (x)} sec (x) tan (x)

Solution steps

\frac{d}{d x} (ln (3 x) - e^{s e c (x)})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (ln (3 x)) - \frac{d}{d x} (e^{s e c (x)})

\frac{d}{d x} (ln (3 x)) = \frac{1}{x}

\frac{d}{d x} (e^{s e c (x)}) = e^{s e c (x)} sec (x) tan (x)

= \frac{1}{x} - e^{s e c (x)} sec (x) tan (x)

What is the derivative of ln(3x-e^{sec(x)}) ?
The derivative of ln(3x-e^{sec(x)}) is 1/x-e^{sec(x)}sec(x)tan(x)
What is the first derivative of ln(3x-e^{sec(x)}) ?
The first derivative of ln(3x-e^{sec(x)}) is 1/x-e^{sec(x)}sec(x)tan(x)