What is (\partial)/(\partial x)(x^5y^5+4x^7y) ?

The answer to (\partial)/(\partial x)(x^5y^5+4x^7y) is 5y^5x^4+28yx^6

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(\partial)/(\partial x)(x^5y^5+4x^7y)

\frac{\partial}{\partial x} (x^{5} y^{5} + 4 x^{7} y)

5 y^{5} x^{4} + 28 y x^{6}

Solution steps

\frac{\partial}{\partial x} (x^{5} y^{5} + 4 x^{7} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{5} y^{5}) + \frac{\partial}{\partial x} (4 x^{7} y)

\frac{\partial}{\partial x} (x^{5} y^{5}) = 5 y^{5} x^{4}

\frac{\partial}{\partial x} (4 x^{7} y) = 28 y x^{6}

= 5 y^{5} x^{4} + 28 y x^{6}

\int \frac{1}{( x - 5 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (\frac{( 3 x - 2 ) ( 2 x - 3 )}{- 2 x ^{2} + 4 x})

x y^{^{'}} + (1 + 2 x) y = 10 e^{- 2 x}

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

\int_{0}^{6} \frac{1}{36 + x ^{2}} d x

What is (\partial)/(\partial x)(x^5y^5+4x^7y) ?
The answer to (\partial)/(\partial x)(x^5y^5+4x^7y) is 5y^5x^4+28yx^6