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Popular >

derivative of xcos(ln(x))

Solution

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

Solution

cos (ln (x)) - sin (ln (x))

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 1 \cdot cos (ln (x)) + (- \frac{sin ( ln ( x ) )}{x}) x

Simplify

1 \cdot cos (ln (x)) + (- \frac{sin ( ln ( x ) )}{x}) x : cos (ln (x)) - sin (ln (x))

= cos (ln (x)) - sin (ln (x))

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of xcos(ln(x)) ?
The derivative of xcos(ln(x)) is cos(ln(x))-sin(ln(x))
What is the first derivative of xcos(ln(x)) ?
The first derivative of xcos(ln(x)) is cos(ln(x))-sin(ln(x))