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Popular >

derivative of (x+y(x-y))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + y, g = x - y

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

\frac{d}{d x} (x + y) = 1 + \frac{d y}{d x}

\frac{d}{d x} (x - y) = 1 - \frac{d y}{d x}

= (1 + \frac{d y}{d x}) (x - y) + (1 - \frac{d y}{d x}) (x + y)

Simplify

(1 + \frac{d y}{d x}) (x - y) + (1 - \frac{d y}{d x}) (x + y) : 2 x - 2 y \frac{d y}{d x}

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

Popular Examples

integral of (2x^2-3x+2)/(x^3-3x^2+2x)

\int \frac{2 x ^{2} - 3 x + 2}{x ^{3} - 3 x ^{2} + 2 x} d x

integral of 1/(2x^2+8x+20)

\int \frac{1}{2 x ^{2} + 8 x + 20} d x

integral of 8^x

\int 8^{x} d x

integral of 4tan^4(x)sec^6(x)

\int 4 tan^{4} (x) sec^{6} (x) d x

integral of (x^2-x+1)/(x^2(x^2+1))

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

Frequently Asked Questions (FAQ)

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