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Popular >

derivative of xcos^2(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos^{2} (x)

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

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

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

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

Simplify

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

Popular Examples

limit as x approaches 1+of 5/(x^2-1)

x \to 1 + lim (\frac{5}{x ^{2} - 1})

integral of 1/(1+2x)

\int \frac{1}{1 + 2 x} d x

limit as x approaches 3 of 4x

x \to 3 lim (4 x)

limit as x approaches 3 of 5x^3-4x^2+x-6

x \to 3 lim (5 x^{3} - 4 x^{2} + x - 6)

derivative of (ax^2+bx+ce^{-x/2})

\frac{d}{d x} ((a x^{2} + b x + c) e^{- \frac{x}{2}})

Frequently Asked Questions (FAQ)

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