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Popular >

derivative of x(cos(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

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

\frac{( x ^{2} - 4 )}{( x ^{2} - 1 )}

integral of (9x^2-8x+8)/(x(x^2+4))

\int \frac{9 x ^{2} - 8 x + 8}{x ( x ^{2} + 4 )} d x

sum from n=0 to infinity of n/(n+2)

n = 0 \sum \infty \frac{n}{n + 2}

derivative of x/(1-2x)

\frac{d}{d x} (\frac{x}{1 - 2 x})

integral of x^3sqrt(x^2+15)

\int x^{3} x^{2} + 15 d x

Frequently Asked Questions (FAQ)

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