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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

\frac{\partial}{\partial x} (4 x^{- \frac{1}{2}} - \frac{6}{x})

\frac{\partial}{\partial x} (ln (9 + x^{2} + 3 y^{2}))

\frac{d}{d x} (\frac{6}{( x - 1 ) ^{4}})

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

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