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Popular >

derivative of x^2cos(x^2)

Solution

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

Solution

2 x cos (x^{2}) - 2 x^{3} sin (x^{2})

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 x cos (x^{2}) + (- sin (x^{2}) \cdot 2 x) x^{2} : 2 x cos (x^{2}) - 2 x^{3} sin (x^{2})

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

Graph

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\int_{0}^{3} y + 1 d y

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f (x) = x^{3} + 3 x - 6, (1, - 2)

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\frac{1}{s - 8}

integral of 8/(x^{-1)+4}

\int \frac{8}{x ^{- 1} + 4} d x

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\int_{0}^{1} \frac{2}{2 - x ^{2}} d x

Frequently Asked Questions (FAQ)

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