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Popular >

derivative of x^2y+xy^2

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

integral from 1 to 2 of 2(1-1/(x^2))

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

(d^2)/(dx^2)((x^2)/(3+4x))

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{3 + 4 x})

derivative of f(x)= x/(x^2+7)derivative of

f (x) = \frac{x}{x ^{2} + 7}

derivative of 3/(4(1-x^{5/2)})

\frac{d}{d x} (\frac{3}{4 ( 1 - x ) ^{\frac{5}{2}}})

4 x^{2} y^{^{''}} + y = 0

Frequently Asked Questions (FAQ)

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