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Popular >

derivative of x^2cos^2(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Graph

Popular Examples

\frac{d y}{d t} = 2 t

derivative of (e^{2x}/(x-3))

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

(dy)/(dt)=e^{-3t},y(0)=10

\frac{d y}{d t} = e^{- 3 t}, y (0) = 10

derivative of (x-1)^2(2x+1)^4 derivative of

(x - 1)^{2} (2 x + 1)^{4}

(\partial)/(\partial x)(e^{x^2-y^2})

\frac{\partial}{\partial x} (e^{x^{2} - y^{2}})

Frequently Asked Questions (FAQ)

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