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Popular >

derivative of (sin(2x)/x)

Solution

\frac{d}{d x} (\frac{sin ( 2 x )}{x})

Solution

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

Solution steps

\frac{d}{d x} (\frac{sin ( 2 x )}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

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

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

Simplify

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

Popular Examples

limit as x approaches 2 of 9-x^2

x \to 2 lim (9 - x^{2})

limit as x approaches-2 of (2x-1)/(x+2)

x \to - 2 lim (\frac{2 x - 1}{x + 2})

3 y^{^{''}} + 12 y = 0

x(dy)/(dx)+3y=(1+x)/(x^3)

x \frac{d y}{d x} + 3 y = \frac{1 + x}{x ^{3}}

integral of 8/(1-cos(4x))

\int \frac{8}{1 - cos ( 4 x )} d x

Frequently Asked Questions (FAQ)

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