What is the derivative of (sin(8x))/(13x) ?

The derivative of (sin(8x))/(13x) is (8xcos(8x)-sin(8x))/(13x^2)

What is the first derivative of (sin(8x))/(13x) ?

The first derivative of (sin(8x))/(13x) is (8xcos(8x)-sin(8x))/(13x^2)

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derivative of

\frac{sin ( 8 x )}{13 x}

\frac{8 x cos ( 8 x ) - sin ( 8 x )}{13 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{sin ( 8 x )}{13 x})

Take the constant out:

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

= \frac{1}{13} \frac{d}{d x} (\frac{sin ( 8 x )}{x})

Apply the Quotient Rule:

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

= \frac{1}{13} \cdot \frac{\frac{d}{d x} ( sin ( 8 x ) ) x - \frac{d x}{d x} sin ( 8 x )}{x ^{2}}

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

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

= \frac{1}{13} \cdot \frac{cos ( 8 x ) \cdot 8 x - 1 \cdot sin ( 8 x )}{x ^{2}}

Simplify

\frac{1}{13} \cdot \frac{cos ( 8 x ) \cdot 8 x - 1 \cdot sin ( 8 x )}{x ^{2}} : \frac{8 x cos ( 8 x ) - sin ( 8 x )}{13 x ^{2}}

= \frac{8 x cos ( 8 x ) - sin ( 8 x )}{13 x ^{2}}

What is the derivative of (sin(8x))/(13x) ?
The derivative of (sin(8x))/(13x) is (8xcos(8x)-sin(8x))/(13x^2)
What is the first derivative of (sin(8x))/(13x) ?
The first derivative of (sin(8x))/(13x) is (8xcos(8x)-sin(8x))/(13x^2)