What is the derivative of x^3+y^3-9xy ?

The derivative of x^3+y^3-9xy is 3x^2+3y^2(dy)/(dx)-9(y+x(dy)/(dx))

What is the first derivative of x^3+y^3-9xy ?

The first derivative of x^3+y^3-9xy is 3x^2+3y^2(dy)/(dx)-9(y+x(dy)/(dx))

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\frac{d}{d x} (x^{3} + y^{3} - 9 x y)

3 x^{2} + 3 y^{2} \frac{d y}{d x} - 9 (y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (x^{3} + y^{3} - 9 x y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3}) + \frac{d}{d x} (y^{3}) - \frac{d}{d x} (9 x y)

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (y^{3}) = 3 y^{2} \frac{d y}{d x}

\frac{d}{d x} (9 x y) = 9 (y + x \frac{d y}{d x})

= 3 x^{2} + 3 y^{2} \frac{d y}{d x} - 9 (y + x \frac{d y}{d x})

What is the derivative of x^3+y^3-9xy ?
The derivative of x^3+y^3-9xy is 3x^2+3y^2(dy)/(dx)-9(y+x(dy)/(dx))
What is the first derivative of x^3+y^3-9xy ?
The first derivative of x^3+y^3-9xy is 3x^2+3y^2(dy)/(dx)-9(y+x(dy)/(dx))