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

The derivative of f(x)=x^2sin(x) is 2xsin(x)+cos(x)x^2

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

The first derivative of f(x)=x^2sin(x) is 2xsin(x)+cos(x)x^2

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derivative of

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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