What is (\partial)/(\partial x)(4x^2y^3+1) ?

The answer to (\partial)/(\partial x)(4x^2y^3+1) is 8xy^3

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(\partial)/(\partial x)(4x^2y^3+1)

\frac{\partial}{\partial x} (4 x^{2} y^{3} + 1)

8 x y^{3}

Solution steps

\frac{\partial}{\partial x} (4 x^{2} y^{3} + 1)

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} (1)

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

\frac{\partial}{\partial x} (1) = 0

= 8 y^{3} x + 0

Simplify

= 8 x y^{3}

\frac{d}{d x} (\frac{3 x + 2}{2 x + 3})

\int e^{2 x} sin (x) d x

\int \frac{16 x ^{2} - 48 x + 15}{2 x ^{3} - 7 x ^{2} + 3 x} d x

e^{0}

\int z 1 - z d z

What is (\partial)/(\partial x)(4x^2y^3+1) ?
The answer to (\partial)/(\partial x)(4x^2y^3+1) is 8xy^3