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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{d}{d x} (- \frac{10 x}{( x ^{2} - 9 ) ^{2}})

sin (cos (x))

x \to 0 - lim (e^{\frac{9}{x}})

x \to \infty lim (x \cdot 0)

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