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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{\partial}{\partial x} (e^{\frac{6}{x}})

\frac{d}{d t} (e^{- t} (2 cos (\frac{t}{2}) - 3 sin (\frac{t}{2})))

(x^{2} + 16) \frac{d y}{d x} + x y - 4 x = 0

\frac{7}{4 x ^{5}}

\frac{d x}{d t} = (\frac{6 x}{2000 + 12 t})

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