What is (\partial)/(\partial x)(8x^3y^2+6xy^4) ?

The answer to (\partial)/(\partial x)(8x^3y^2+6xy^4) is 24y^2x^2+6y^4

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(\partial)/(\partial x)(8x^3y^2+6xy^4)

\frac{\partial}{\partial x} (8 x^{3} y^{2} + 6 x y^{4})

24 y^{2} x^{2} + 6 y^{4}

Solution steps

\frac{\partial}{\partial x} (8 x^{3} y^{2} + 6 x y^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 x^{3} y^{2}) + \frac{\partial}{\partial x} (6 x y^{4})

\frac{\partial}{\partial x} (8 x^{3} y^{2}) = 24 y^{2} x^{2}

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

= 24 y^{2} x^{2} + 6 y^{4}

d er i v a t i v e f (x) = x e^{y} - 5 y = 2 x - 6 - 2 e^{2}

\int arctanh (x) d x

\int \frac{x ^{2}}{e ^{3 x}} d x

a re a x = 7 y^{2}, x = 4 + 6 y^{2}

\frac{d}{d x} (\frac{- 2 ln ( x ) + 1}{x ^{3}})

What is (\partial)/(\partial x)(8x^3y^2+6xy^4) ?
The answer to (\partial)/(\partial x)(8x^3y^2+6xy^4) is 24y^2x^2+6y^4