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

The derivative of (sin^3(x))/(ln(x^3)) is (3xsin^2(x)cos(x)ln(x^3)-3sin^3(x))/(xln^2(x^3))

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

The first derivative of (sin^3(x))/(ln(x^3)) is (3xsin^2(x)cos(x)ln(x^3)-3sin^3(x))/(xln^2(x^3))

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derivative of

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

\frac{3 x sin ^{2} ( x ) cos ( x ) ln ( x ^{3} ) - 3 sin ^{3} ( x )}{x ln ^{2} ( x ^{3} )}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( sin ^{3} ( x ) ) ln ( x ^{3} ) - \frac{d}{d x} ( ln ( x ^{3} ) ) sin ^{3} ( x )}{( ln ( x ^{3} ) ) ^{2}}

\frac{d}{d x} (sin^{3} (x)) = 3 sin^{2} (x) cos (x)

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

= \frac{3 sin ^{2} ( x ) cos ( x ) ln ( x ^{3} ) - \frac{3}{x} sin ^{3} ( x )}{( ln ( x ^{3} ) ) ^{2}}

Simplify

\frac{3 sin ^{2} ( x ) cos ( x ) ln ( x ^{3} ) - \frac{3}{x} sin ^{3} ( x )}{ln ^{2} ( x ^{3} )} : \frac{3 x sin ^{2} ( x ) cos ( x ) ln ( x ^{3} ) - 3 sin ^{3} ( x )}{x ln ^{2} ( x ^{3} )}

= \frac{3 x sin ^{2} ( x ) cos ( x ) ln ( x ^{3} ) - 3 sin ^{3} ( x )}{x ln ^{2} ( x ^{3} )}

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

\frac{d}{d t} (3 t^{3} - 2 t^{2} + t - 5)

- 10 cos^{6} (x)

x^{1} - d

\frac{x ^{4}}{4 + x ^{33} + x ^{22}}

What is the derivative of (sin^3(x))/(ln(x^3)) ?
The derivative of (sin^3(x))/(ln(x^3)) is (3xsin^2(x)cos(x)ln(x^3)-3sin^3(x))/(xln^2(x^3))
What is the first derivative of (sin^3(x))/(ln(x^3)) ?
The first derivative of (sin^3(x))/(ln(x^3)) is (3xsin^2(x)cos(x)ln(x^3)-3sin^3(x))/(xln^2(x^3))