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Popular >

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

Solution

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

Solution

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

Solution steps

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

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

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

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

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

Popular Examples

(\partial)/(\partial x)(4sin(x))

\frac{\partial}{\partial x} (4 sin (x))

integral from-2 to 1 of (x+1)sqrt(x+3)

\int_{- 2}^{1} (x + 1) x + 3 d x

derivative of x^3+2x-1 derivative of

x^{3} + 2 x - 1

derivative of F(x)=7x^6(x^4-7x)derivative of

F (x) = 7 x^{6} (x^{4} - 7 x)

derivative of tan(sqrt(3x))

\frac{d}{d x} (tan (3 x))

Frequently Asked Questions (FAQ)

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