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Popular >

derivative of x^2+y^2-2xy

Solution

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

Solution

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

Solution steps

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

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

Popular Examples

integral of 1/(t^2)

\int \frac{1}{t ^{2}} d t

derivative of (sin(3x)/(1+x^2))

\frac{d}{d x} (\frac{sin ( 3 x )}{1 + x ^{2}})

(\partial)/(\partial x)(10cos(x)y^2z)

\frac{\partial}{\partial x} (10 cos (x) y^{2} z)

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

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

(\partial)/(\partial y)(9e^xln(y))

\frac{\partial}{\partial y} (9 e^{x} ln (y))

Frequently Asked Questions (FAQ)

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