What is the derivative of y=(sin(3x))ln(x) ?

The derivative of y=(sin(3x))ln(x) is 3cos(3x)ln(x)+(sin(3x))/x

What is the first derivative of y=(sin(3x))ln(x) ?

The first derivative of y=(sin(3x))ln(x) is 3cos(3x)ln(x)+(sin(3x))/x

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derivative of

y = (sin (3 x)) ln (x)

3 cos (3 x) ln (x) + \frac{sin ( 3 x )}{x}

Solution steps

\frac{d}{d x} (sin (3 x) ln (x))

Apply the Product Rule:

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

f = sin (3 x), g = ln (x)

= \frac{d}{d x} (sin (3 x)) ln (x) + \frac{d}{d x} (ln (x)) sin (3 x)

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= cos (3 x) \cdot 3 ln (x) + \frac{1}{x} sin (3 x)

\frac{1}{x} sin (3 x) = \frac{sin ( 3 x )}{x}

= 3 cos (3 x) ln (x) + \frac{sin ( 3 x )}{x}

\frac{d}{d x} (48 x^{\frac{1}{2}})

\int \frac{8}{x ^{2} ( x ^{2} + 25 )} d x

f (x) = \frac{2}{ln ( x )}

x^{2} y y^{^{'}} = ey

What is the derivative of y=(sin(3x))ln(x) ?
The derivative of y=(sin(3x))ln(x) is 3cos(3x)ln(x)+(sin(3x))/x
What is the first derivative of y=(sin(3x))ln(x) ?
The first derivative of y=(sin(3x))ln(x) is 3cos(3x)ln(x)+(sin(3x))/x