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

The derivative of x^3+3xy+y^3 is 3x^2+3y

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

The first derivative of x^3+3xy+y^3 is 3x^2+3y

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derivative of

x^{3} + 3 x y + y^{3}

3 x^{2} + 3 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{d}{d x} (y^{3}) = 0

= 3 x^{2} + 3 y + 0

Simplify

= 3 x^{2} + 3 y

What is the derivative of x^3+3xy+y^3 ?
The derivative of x^3+3xy+y^3 is 3x^2+3y
What is the first derivative of x^3+3xy+y^3 ?
The first derivative of x^3+3xy+y^3 is 3x^2+3y