What is (\partial)/(\partial x)(2x^4y+16y^3) ?

The answer to (\partial)/(\partial x)(2x^4y+16y^3) is 8x^3y

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(\partial)/(\partial x)(2x^4y+16y^3)

\frac{\partial}{\partial x} (2 x^{4} y + 16 y^{3})

8 x^{3} y

Solution steps

\frac{\partial}{\partial x} (2 x^{4} y + 16 y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{4} y) + \frac{\partial}{\partial x} (16 y^{3})

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

\frac{\partial}{\partial x} (16 y^{3}) = 0

= 8 y x^{3} + 0

Simplify

= 8 x^{3} y

y = \frac{1}{ln ( x )}

\int 51 sec^{4} (x) d x

\int \frac{2 x}{( x - 1 ) ^{5}} d x

\frac{d}{d x} (\frac{3}{1 - x})

f (t) = ln (t)

What is (\partial)/(\partial x)(2x^4y+16y^3) ?
The answer to (\partial)/(\partial x)(2x^4y+16y^3) is 8x^3y