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

The derivative of x^2cos(ln(x)) is 2xcos(ln(x))-xsin(ln(x))

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

The first derivative of x^2cos(ln(x)) is 2xcos(ln(x))-xsin(ln(x))

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 2 x cos (ln (x)) - x sin (ln (x))

x \to 0 + lim (x \cdot e^{\frac{1}{x}})

\int \frac{x}{1 - 3 x ^{2}} d x

\int 5 cot^{5} (x) sin^{4} (x) d x

\int t 2 t^{2} + 3 d t

x \to \infty lim (- x e^{x})

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