What is the derivative of (sin(6x^3)/(5x)) ?

The derivative of (sin(6x^3)/(5x)) is (2sin(6)x)/5

What is the first derivative of (sin(6x^3)/(5x)) ?

The first derivative of (sin(6x^3)/(5x)) is (2sin(6)x)/5

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\frac{d}{d x} (\frac{sin ( 6 ) x ^{3}}{5 x})

\frac{2 sin ( 6 ) x}{5}

Solution steps

\frac{d}{d x} (\frac{sin ( 6 ) x ^{3}}{5 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{sin ( 6 )}{5} \frac{d}{d x} (\frac{x ^{3}}{x})

Apply the Quotient Rule:

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

= \frac{sin ( 6 )}{5} \cdot \frac{\frac{d}{d x} ( x ^{3} ) x - \frac{d x}{d x} x ^{3}}{x ^{2}}

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

\frac{d x}{d x} = 1

= \frac{sin ( 6 )}{5} \cdot \frac{3 x ^{2} x - 1 \cdot x ^{3}}{x ^{2}}

Simplify

\frac{sin ( 6 )}{5} \cdot \frac{3 x ^{2} x - 1 \cdot x ^{3}}{x ^{2}} : \frac{2 sin ( 6 ) x}{5}

= \frac{2 sin ( 6 ) x}{5}

\int x (ln (x + 1)) d x

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\frac{d}{d x} (x^{\frac{1}{4}} - 4 e^{x})

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What is the derivative of (sin(6x^3)/(5x)) ?
The derivative of (sin(6x^3)/(5x)) is (2sin(6)x)/5
What is the first derivative of (sin(6x^3)/(5x)) ?
The first derivative of (sin(6x^3)/(5x)) is (2sin(6)x)/5