What is (\partial)/(\partial x)(xln(ycos(x))) ?

The answer to (\partial)/(\partial x)(xln(ycos(x))) is ln(ycos(x))-xtan(x)

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(\partial)/(\partial x)(xln(ycos(x)))

\frac{\partial}{\partial x} (x ln (y cos (x)))

ln (y cos (x)) - x tan (x)

Solution steps

\frac{\partial}{\partial x} (x ln (y cos (x)))

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = ln (y cos (x))

= \frac{\partial}{\partial x} (x) ln (y cos (x)) + \frac{\partial}{\partial x} (ln (y cos (x))) x

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

\frac{\partial}{\partial x} (ln (y cos (x))) = - tan (x)

= 1 \cdot ln (y cos (x)) + (- tan (x)) x

Simplify

= ln (y cos (x)) - x tan (x)

\frac{d}{d x} (x^{4} - 10 x^{2} + 9)

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

\int \frac{x + 20}{x ^{2} + 18 x + 85} d x

\int sin^{2} (2 x) cos (x) d x

\frac{d}{d x} (e^{y} cos (x))

What is (\partial)/(\partial x)(xln(ycos(x))) ?
The answer to (\partial)/(\partial x)(xln(ycos(x))) is ln(ycos(x))-xtan(x)