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Popular >

derivative of xcos(x^2)

Solution

derivative of

x cos (x^{2})

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Popular Examples

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\frac{d}{d x} (\frac{x + 6}{5 x ^{2} e ^{x}})

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x \to 16 lim (x - 164)

(\partial)/(\partial x)(arctan(x^2+y^2))

\frac{\partial}{\partial x} (arctan (x^{2} + y^{2}))

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\frac{x ^{5}}{4 - x ^{4}}

Frequently Asked Questions (FAQ)

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