What is (\partial)/(\partial y)(4x^3y^3-3) ?

The answer to (\partial)/(\partial y)(4x^3y^3-3) is 12x^3y^2

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(\partial)/(\partial y)(4x^3y^3-3)

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 3)

12 x^{3} y^{2}

Solution steps

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 3)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (4 x^{3} y^{3}) - \frac{\partial}{\partial y} (3)

\frac{\partial}{\partial y} (4 x^{3} y^{3}) = 12 x^{3} y^{2}

\frac{\partial}{\partial y} (3) = 0

= 12 x^{3} y^{2} - 0

Simplify

= 12 x^{3} y^{2}

\int_{- 1}^{1} x^{2} x^{3} + 1 d x

\int \frac{x ^{2} + 3 x}{x + 4} d x

\int (\frac{e ^{4 x} - 5}{e ^{2 x}}) d x

y^{^{'}} - \frac{5}{x} y = \frac{y ^{5}}{x ^{3}}, y (1) = 1

f (x) = (x^{2} - 5)^{2}

What is (\partial)/(\partial y)(4x^3y^3-3) ?
The answer to (\partial)/(\partial y)(4x^3y^3-3) is 12x^3y^2