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Popular >

derivative of x^2+y^2+xy

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Popular Examples

area y=2x-2x^2,[0,1]area

y = 2 x - 2 x^{2}, [0, 1]

area y= 1/(x^2),y=0,x=1,x=5 area

y = \frac{1}{x ^{2}}, y = 0, x = 1, x = 5

limit as x approaches 0 of (sin(2x))/x+4

x \to 0 lim (\frac{sin ( 2 x )}{x} + 4)

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

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

limit as x approaches infinity of x^2+3

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

Frequently Asked Questions (FAQ)

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