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Popular >

derivative of (x^3y+xy^3/(x^2+y^2))

Solution

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

Solution

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

Solution steps

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

Simplify

\frac{x ^{3} y + x y ^{3}}{x ^{2} + y ^{2}} : x y

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

Apply the Product Rule:

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

f = x, g = y

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

\frac{d x}{d x} = 1

= 1 \cdot y + \frac{d y}{d x} x

Simplify

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

Popular Examples

tangent of f(x)=sqrt(x-4),(13,3)tangent of

f (x) = x - 4, (13, 3)

tangent of f(x)= 5/(x+1),\at x=(-1)/3 tangent of

f (x) = \frac{5}{x + 1}, at x = \frac{- 1}{3}

limit as x approaches 0 of (0+5)/(3(0))

x \to 0 lim (\frac{0 + 5}{3 ( 0 )})

derivative of f(x)=(x^2+8x+3)/(sqrt(x))derivative of

f (x) = \frac{x ^{2} + 8 x + 3}{x}

limit as x approaches infinity of (x^2+2x+5)/(e^{3x)}

x \to \infty lim (\frac{x ^{2} + 2 x + 5}{e ^{3 x}})

Frequently Asked Questions (FAQ)

What is the derivative of (x^3y+xy^3/(x^2+y^2)) ?
The derivative of (x^3y+xy^3/(x^2+y^2)) is y+x(dy)/(dx)
What is the first derivative of (x^3y+xy^3/(x^2+y^2)) ?
The first derivative of (x^3y+xy^3/(x^2+y^2)) is y+x(dy)/(dx)