What is the derivative of f(x)=x^2cos(x) ?

The derivative of f(x)=x^2cos(x) is 2xcos(x)-x^2sin(x)

What is the first derivative of f(x)=x^2cos(x) ?

The first derivative of f(x)=x^2cos(x) is 2xcos(x)-x^2sin(x)

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derivative

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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