What is the derivative of (ln(x)^2cos(x)) ?

The derivative of (ln(x)^2cos(x)) is (2ln(x)cos(x))/x-ln^2(x)sin(x)

What is the first derivative of (ln(x)^2cos(x)) ?

The first derivative of (ln(x)^2cos(x)) is (2ln(x)cos(x))/x-ln^2(x)sin(x)

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\frac{d}{d x} ((ln (x))^{2} cos (x))

\frac{2 ln ( x ) cos ( x )}{x} - ln^{2} (x) sin (x)

Solution steps

\frac{d}{d x} ((ln (x))^{2} cos (x))

Apply the Product Rule:

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

f = (ln (x))^{2}, g = cos (x)

= \frac{d}{d x} ((ln (x))^{2}) cos (x) + \frac{d}{d x} (cos (x)) (ln (x))^{2}

\frac{d}{d x} ((ln (x))^{2}) = \frac{2 ln ( x )}{x}

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

= \frac{2 ln ( x )}{x} cos (x) + (- sin (x)) (ln (x))^{2}

Simplify

\frac{2 ln ( x )}{x} cos (x) + (- sin (x)) ln^{2} (x) : \frac{2 ln ( x ) cos ( x )}{x} - ln^{2} (x) sin (x)

= \frac{2 ln ( x ) cos ( x )}{x} - ln^{2} (x) sin (x)

What is the derivative of (ln(x)^2cos(x)) ?
The derivative of (ln(x)^2cos(x)) is (2ln(x)cos(x))/x-ln^2(x)sin(x)
What is the first derivative of (ln(x)^2cos(x)) ?
The first derivative of (ln(x)^2cos(x)) is (2ln(x)cos(x))/x-ln^2(x)sin(x)