What is (\partial)/(\partial y)(4x^2y^3+4) ?

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

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(\partial)/(\partial y)(4x^2y^3+4)

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

12 x^{2} y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (4) = 0

= 12 x^{2} y^{2} + 0

Simplify

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

\frac{d}{d t} (t^{2} sin (wt))

\int \frac{1}{( x ^{2} + 3 ) ^{\frac{3}{2}}} d x

\int \frac{1}{9 x ^{2} + 36 x + 35} d x

y = \frac{8 x}{x ^{2} - 1}, (3, 3)

y^{^{''}} + 625 y = sec (25 x)

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