What is the derivative of f(x)=(sin(x))/x ?

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

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

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

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derivative of

f (x) = \frac{sin ( x )}{x}

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

Solution steps

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

Simplify

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

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