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Popular >

derivative of x^2-xy+y^2

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

integral from 0 to 1 of (63)/(4y-1)

\int_{0}^{1} \frac{63}{4 y - 1} d y

derivative of e^x(3x^2-6x+6)derivative of

e^{x} (3 x^{2} - 6 x + 6)

limit as x approaches 0-of 7-2sqrt(x)

x \to 0 - lim (7 - 2 x)

integral of 3x^3-5x^2+3x+4

\int 3 x^{3} - 5 x^{2} + 3 x + 4 d x

derivative of (x+1)^{x+1}derivative of

(x + 1)^{x + 1}

Frequently Asked Questions (FAQ)

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