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

The derivative of (sin(x)/(3x)) is (xcos(x)-sin(x))/(3x^2)

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

The first derivative of (sin(x)/(3x)) is (xcos(x)-sin(x))/(3x^2)

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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