What is (\partial)/(\partial x)(x^9y^9+5x^8y) ?

The answer to (\partial)/(\partial x)(x^9y^9+5x^8y) is 9y^9x^8+40yx^7

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(\partial)/(\partial x)(x^9y^9+5x^8y)

\frac{\partial}{\partial x} (x^{9} y^{9} + 5 x^{8} y)

9 y^{9} x^{8} + 40 y x^{7}

Solution steps

\frac{\partial}{\partial x} (x^{9} y^{9} + 5 x^{8} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{9} y^{9}) + \frac{\partial}{\partial x} (5 x^{8} y)

\frac{\partial}{\partial x} (x^{9} y^{9}) = 9 y^{9} x^{8}

\frac{\partial}{\partial x} (5 x^{8} y) = 40 y x^{7}

= 9 y^{9} x^{8} + 40 y x^{7}

y^{^{''}} - y - 4 = 0

x \to - 3 lim (F (x))

\int \frac{6}{( 2 x - 1 ) ^{2}} d x

\frac{d}{d x} (\frac{x}{x + 20})

\int \frac{2 x}{x + 2} d x

What is (\partial)/(\partial x)(x^9y^9+5x^8y) ?
The answer to (\partial)/(\partial x)(x^9y^9+5x^8y) is 9y^9x^8+40yx^7