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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to \infty + lim (5 + \frac{6}{x})

2 \frac{d ^{2} y}{d x ^{2}} - 14 \frac{d y}{d x} + 24 y = 3 sin (4 x)

x \to 2 - lim (e^{\frac{3}{( 2 - x )}})

\frac{d y}{d x} = 6 y e^{x + 2}

x^{4} - 2 x^{2}, 2 x^{2}, [- 2, 0]

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