What is the derivative of (x^3-y^3/(x-y)) ?

The derivative of (x^3-y^3/(x-y)) is 2x+y+x(dy)/(dx)+2y(dy)/(dx)

What is the first derivative of (x^3-y^3/(x-y)) ?

The first derivative of (x^3-y^3/(x-y)) is 2x+y+x(dy)/(dx)+2y(dy)/(dx)

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\frac{d}{d x} (\frac{x ^{3} - y ^{3}}{x - y})

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

Solution steps

\frac{d}{d x} (\frac{x ^{3} - y ^{3}}{x - y})

Simplify

\frac{x ^{3} - y ^{3}}{x - y} : x^{2} + x y + y^{2}

= \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}

x \to 0 lim (+ (x^{x}))

y^{^{'}} = 7 t y^{2}

\frac{ln ( x )}{x ^{5}}

θ \to 0 lim (\frac{sin ( 7 θ )}{θ})

x^{2} - 5 x + 9

What is the derivative of (x^3-y^3/(x-y)) ?
The derivative of (x^3-y^3/(x-y)) is 2x+y+x(dy)/(dx)+2y(dy)/(dx)
What is the first derivative of (x^3-y^3/(x-y)) ?
The first derivative of (x^3-y^3/(x-y)) is 2x+y+x(dy)/(dx)+2y(dy)/(dx)