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

The answer to (\partial)/(\partial y)(4x^3y^2+4) is 8x^3y

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

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

8 x^{3} y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (4 x^{3} y^{2}) = 8 x^{3} y

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

= 8 x^{3} y + 0

Simplify

= 8 x^{3} y

4 - 4 x^{2}, x^{8} - 1

\frac{\partial}{\partial s} (\frac{( s - 2 r )}{t})

\int \frac{x ^{2}}{5} d x

f (x) = \frac{6 x ^{\frac{3}{2}}}{x}

\int \frac{1 - 3 x + 6 x ^{2}}{( x ^{2} + 1 ) ( 4 x + 1 )} d x

What is (\partial)/(\partial y)(4x^3y^2+4) ?
The answer to (\partial)/(\partial y)(4x^3y^2+4) is 8x^3y