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Popular >

derivative of (xy^2)

Solution

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

Solution

2 x y^{2} + 2 y \frac{d y}{d x} x^{2}

Solution steps

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

Simplify

(x y)^{2} : x^{2} y^{2}

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

Apply the Product Rule:

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

f = x^{2}, g = y^{2}

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

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

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

= 2 x y^{2} + 2 y \frac{d y}{d x} x^{2}

Popular Examples

derivative of (-xsin(x)-cos(x))/(4x^2)derivative of

\frac{- x sin ( x ) - cos ( x )}{4 x ^{2}}

integral of x^2-6x+5

\int x^{2} - 6 x + 5 d x

(\partial)/(\partial x)(sqrt(2x^2+5y^2))

\frac{\partial}{\partial x} (2 x^{2} + 5 y^{2})

tangent of y=2x^3-2x(-1)tangent of

y = 2 x^{3} - 2 x (- 1)

derivative of 2cos(-2x)

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

Frequently Asked Questions (FAQ)

What is the derivative of (xy^2) ?
The derivative of (xy^2) is 2xy^2+2y(dy)/(dx)x^2
What is the first derivative of (xy^2) ?
The first derivative of (xy^2) is 2xy^2+2y(dy)/(dx)x^2