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

The derivative of sin(ln(x^3)) is (3cos(3ln(x)))/x

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

The first derivative of sin(ln(x^3)) is (3cos(3ln(x)))/x

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

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

Solution steps

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

Apply the chain rule:

cos (ln (x^{3})) \frac{d}{d x} (ln (x^{3}))

= cos (ln (x^{3})) \frac{d}{d x} (ln (x^{3}))

\frac{d}{d x} (ln (x^{3})) = \frac{3}{x}

= cos (ln (x^{3})) \frac{3}{x}

Simplify

cos (ln (x^{3})) \frac{3}{x} : \frac{3 cos ( 3 ln ( x ) )}{x}

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

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