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

The answer to (\partial)/(\partial x)(3x^2y^4+2) is 6xy^4

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

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

6 x y^{4}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (3 x^{2} y^{4}) = 6 y^{4} x

\frac{\partial}{\partial x} (2) = 0

= 6 y^{4} x + 0

Simplify

= 6 x y^{4}

\int e^{y^{3}} d y

\frac{d}{d x} (r (x) (x)^{2} e^{r (x) x})

2 y^{^{''}} + 2 y^{^{'}} + y = 0

\frac{\partial}{\partial y} (\frac{x - y}{x})

\int 3 x e^{3 z} + 5 d z

What is (\partial)/(\partial x)(3x^2y^4+2) ?
The answer to (\partial)/(\partial x)(3x^2y^4+2) is 6xy^4