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

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

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

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

3 x^{4} y^{2} + 8 x^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 3 x^{4} y^{2} + 8 x^{2}

f^{^{'''}} + f^{^{''}} + 3 f^{^{'}} - 5 f = 0

s - 1

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

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

x \to 3 - lim (\frac{1}{∣ x - 3 ∣})

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