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Popular >

derivative of (sin(x)/x)

Solution

\frac{d}{d 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

integral of 11z^3e^z

\int 11 z^{3} e^{z} d z

laplacetransform 2e^{t/2}laplace transform

2 e^{\frac{t}{2}}

integral from 0 to 1 of ysqrt(1-y^2)

\int_{0}^{1} y 1 - y^{2} d y

derivative of y=arctan(1)-x^1+x derivative of

y = arctan (1) - x^{1} + x

integral from 2 to t of 1/((5x^5))

\int_{2}^{t} \frac{1}{( 5 x ^{5} )} d x

Frequently Asked Questions (FAQ)

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