What is the derivative of (sin(2x)/(5x^2)) ?

The derivative of (sin(2x)/(5x^2)) is (2(xcos(2x)-sin(2x)))/(5x^3)

What is the first derivative of (sin(2x)/(5x^2)) ?

The first derivative of (sin(2x)/(5x^2)) is (2(xcos(2x)-sin(2x)))/(5x^3)

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\frac{d}{d x} (\frac{sin ( 2 x )}{5 x ^{2}})

\frac{2 ( x cos ( 2 x ) - sin ( 2 x ) )}{5 x ^{3}}

Solution steps

\frac{d}{d x} (\frac{sin ( 2 x )}{5 x ^{2}})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{sin ( 2 x )}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( sin ( 2 x ) ) x ^{2} - \frac{d}{d x} ( x ^{2} ) sin ( 2 x )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{5} \cdot \frac{cos ( 2 x ) \cdot 2 x ^{2} - 2 x sin ( 2 x )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{cos ( 2 x ) \cdot 2 x ^{2} - 2 x sin ( 2 x )}{( x ^{2} ) ^{2}} : \frac{2 ( x cos ( 2 x ) - sin ( 2 x ) )}{5 x ^{3}}

= \frac{2 ( x cos ( 2 x ) - sin ( 2 x ) )}{5 x ^{3}}

\int 6 x^{3} e^{- x^{2}} d x

\frac{d}{d z} (cos (z))

x \to 0 lim (π)

y = ln (\frac{7 + e ^{x}}{7 - e ^{x}})

\int cos^{2} (d) x d x

What is the derivative of (sin(2x)/(5x^2)) ?
The derivative of (sin(2x)/(5x^2)) is (2(xcos(2x)-sin(2x)))/(5x^3)
What is the first derivative of (sin(2x)/(5x^2)) ?
The first derivative of (sin(2x)/(5x^2)) is (2(xcos(2x)-sin(2x)))/(5x^3)