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Popular >

derivative of x^2-4xy+y^2

Solution

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

Solution

2 x - 4 (y + x \frac{d y}{d x}) + 2 y \frac{d y}{d x}

Solution steps

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

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

\frac{d}{d x} (4 x y) = 4 (y + x \frac{d y}{d x})

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

= 2 x - 4 (y + x \frac{d y}{d x}) + 2 y \frac{d y}{d x}

Popular Examples

x^{2} y^{^{'}} + x y = 9

derivative of ln(x(x-1))

\frac{d}{d x} (ln (x) (x - 1))

implicit (dy)/(dx),5cos(8x)sin(5y)=8 implicit derivative

\frac{d y}{d x}, 5 cos (8 x) sin (5 y) = 8

y^{^{''}} = 12 t - 2

derivative of (6x^2+3x+7)/(sqrt(x))derivative of

\frac{6 x ^{2} + 3 x + 7}{x}

Frequently Asked Questions (FAQ)

What is the derivative of x^2-4xy+y^2 ?
The derivative of x^2-4xy+y^2 is 2x-4(y+x(dy)/(dx))+2y(dy)/(dx)
What is the first derivative of x^2-4xy+y^2 ?
The first derivative of x^2-4xy+y^2 is 2x-4(y+x(dy)/(dx))+2y(dy)/(dx)