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Popular >

derivative of x^{(2)}sin(x)

Solution

derivative of

x^{(2)} sin (x)

Solution

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}

Popular Examples

integral from 0 to pi/2 of sin^3(3x)

\int_{0}^{\frac{π}{2}} sin^{3} (3 x) d x

tangent of (2x-1)^2ln(2x-1)tangent of

(2 x - 1)^{2} ln (2 x - 1)

(dy)/(dx)=y(1-y),y(0)=2

\frac{d y}{d x} = y (1 - y), y (0) = 2

derivative of (-2x^2+2/((1+x^2)^2))

\frac{d}{d x} (\frac{- 2 x ^{2} + 2}{( 1 + x ^{2} ) ^{2}})

(\partial)/(\partial x)(-4y(-2x-y-3))

\frac{\partial}{\partial x} (- 4 y (- 2 x - y - 3))

Frequently Asked Questions (FAQ)

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