What is the derivative of cos(xx^2) ?

The derivative of cos(xx^2) is -x^2sin(x)+2xcos(x)

What is the first derivative of cos(xx^2) ?

The first derivative of cos(xx^2) is -x^2sin(x)+2xcos(x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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