What is (\partial)/(\partial y)(2y^3-6y+x^2) ?

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

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(\partial)/(\partial y)(2y^3-6y+x^2)

\frac{\partial}{\partial y} (2 y^{3} - 6 y + x^{2})

6 y^{2} - 6

Solution steps

\frac{\partial}{\partial y} (2 y^{3} - 6 y + x^{2})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (2 y^{3}) - \frac{\partial}{\partial y} (6 y) + \frac{\partial}{\partial y} (x^{2})

\frac{\partial}{\partial y} (2 y^{3}) = 6 y^{2}

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

\frac{\partial}{\partial y} (x^{2}) = 0

= 6 y^{2} - 6 + 0

Simplify

= 6 y^{2} - 6

ln (5)

x \to + 0 + lim (\frac{1}{x} - \frac{1}{x ^{2} + x})

\frac{\partial}{\partial x} (e^{\frac{y}{x}} - y \cdot e^{- x})

x \to 0 lim (x^{4} sin (\frac{4}{x}))

\frac{1 + 4 s}{s ( 2 s ^{2} + 2 s + 1 )}

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