What is (\partial)/(\partial x)(x^3+8y^3-6xy+5) ?

The answer to (\partial)/(\partial x)(x^3+8y^3-6xy+5) is 3x^2-6y

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(\partial)/(\partial x)(x^3+8y^3-6xy+5)

\frac{\partial}{\partial x} (x^{3} + 8 y^{3} - 6 x y + 5)

3 x^{2} - 6 y

Solution steps

\frac{\partial}{\partial x} (x^{3} + 8 y^{3} - 6 x y + 5)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (8 y^{3}) - \frac{\partial}{\partial x} (6 x y) + \frac{\partial}{\partial x} (5)

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

\frac{\partial}{\partial x} (8 y^{3}) = 0

\frac{\partial}{\partial x} (6 x y) = 6 y

\frac{\partial}{\partial x} (5) = 0

= 3 x^{2} + 0 - 6 y + 0

Simplify

= 3 x^{2} - 6 y

x \to - 1 - lim (x^{3} - 3)

\frac{d}{d x} (3 a x^{2} + 2 b x + c)

\int (4 x^{2} - 2) x d x

y = sin (sin (x)), (3 π, 0)

\frac{\partial}{\partial x} (sin (x^{2} - 5 x y))

What is (\partial)/(\partial x)(x^3+8y^3-6xy+5) ?
The answer to (\partial)/(\partial x)(x^3+8y^3-6xy+5) is 3x^2-6y