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

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

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

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

8 x y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 8 y^{3} x + 0

Simplify

= 8 x y^{3}

\int \frac{1}{4 - e ^{2 x}} d x

sin^{2} (x) + cos (x)

\int \frac{1}{1 - 2 v} d v

e^{2 x}, 5

\frac{d y}{d x} = 2 x y^{2}

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