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Popular >

derivative of (cos^2(x)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

Popular Examples

integral of ((5-x)/x)^2

\int (\frac{5 - x}{x})^{2} d x

integral of sqrt(x)(1-sqrt(x))

\int x (1 - x) d x

derivative of ln(ln(14x))

\frac{d}{d x} (ln (ln (14 x)))

(\partial)/(\partial x)(sqrt(|xy|))

\frac{\partial}{\partial x} (∣ x y ∣)

(dy)/(dx)+y/x =x^2

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

Frequently Asked Questions (FAQ)

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