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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d y}{d x} = (x - 3) (y + 1)^{\frac{2}{3}}

\int \frac{4 x}{( 2 x ^{2} - 8 ) ^{5}} d x

\frac{d}{d x} ((\frac{3}{2})^{x})

y y^{^{'}} = t^{2}, y (0) = 2

y^{^{'}} + 3 y = 1, y (0) = 1

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