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Popular >

derivative of f(x)=(sin(x))/x

Solution

derivative of

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

Solution

\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}}

Popular Examples

derivative of x^3-9x^2+24x+1

\frac{d}{d x} (x^{3} - 9 x^{2} + 24 x + 1)

integral of (x+4)^2(x-2)

\int (x + 4)^{2} (x - 2) d x

f(x)=arcsec(x)+arccsc(x)

f (x) = arcsec (x) + arccsc (x)

derivative of (x^3/(30)+5/(2x))

\frac{d}{d x} (\frac{x ^{3}}{30} + \frac{5}{2 x})

integral of cot^3(7x)

\int cot^{3} (7 x) d x

Frequently Asked Questions (FAQ)

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)