What is the derivative of x-ln(e^xcos(x)) ?

The derivative of x-ln(e^xcos(x)) is tan(x)

What is the first derivative of x-ln(e^xcos(x)) ?

The first derivative of x-ln(e^xcos(x)) is tan(x)

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\frac{d}{d x} (x - ln (e^{x} cos (x)))

tan (x)

Solution steps

\frac{d}{d x} (x - ln (e^{x} cos (x)))

Apply the Sum/Difference Rule:

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

= \frac{d x}{d x} - \frac{d}{d x} (ln (e^{x} cos (x)))

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

\frac{d}{d x} (ln (e^{x} cos (x))) = 1 - tan (x)

= 1 - (1 - tan (x))

Simplify

= tan (x)

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

\frac{d}{d x} (\frac{x ^{2}}{2 x + 1})

\frac{d}{d y} (x^{2} - y^{2})

n = 1 \sum \infty \frac{n}{n ^{3} + 2}

What is the derivative of x-ln(e^xcos(x)) ?
The derivative of x-ln(e^xcos(x)) is tan(x)
What is the first derivative of x-ln(e^xcos(x)) ?
The first derivative of x-ln(e^xcos(x)) is tan(x)