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

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

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

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

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

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

Solution steps

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

Simplify

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

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

Take the constant out:

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

= - \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)) = sin (2 x)

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

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

Simplify

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

e^{6 x}

y^{^{''}} - 3 y^{^{'}} + 2 y = 1 + 2 e^{3 t}

t^{2} sin (\frac{1}{2} t)

n = 0 \sum \infty n^{n} x^{n}

x \to 0 lim (\frac{3 - 3 cos ( x )}{sin ^{2} ( x )})

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