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Popular Calculus >

derivative of xsin(x^2)

Solution

derivative of

x sin (x^{2})

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of xsin(x^2) ?
The derivative of xsin(x^2) is sin(x^2)+2x^2cos(x^2)
What is the first derivative of xsin(x^2) ?
The first derivative of xsin(x^2) is sin(x^2)+2x^2cos(x^2)