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

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

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

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

4 x^{3} y^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (y^{4}) = 0

= 4 y^{3} x^{3} - 0

Simplify

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

\frac{d}{d y} (ln (x + 2 y + 3 z))

x \to 5 - lim (\frac{2}{x - 5} + 1)

- 4 x^{2} + 1

\frac{\partial}{\partial y} (sin (x^{5} - 7 y))

\frac{d y}{d x} = (\frac{4}{x ^{2} + 1}) (y + 1)

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