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

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

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

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

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derivative of

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}

\frac{d y}{d x} = y \cdot (\frac{1}{x} - y)

\frac{\partial}{\partial u} (\frac{v}{u})

\frac{d}{d x} (ln (\frac{9 - x}{5 + x}))

- 9 x^{2}

\frac{d}{d x} (arccos (cos (x)))

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