What is (\partial)/(\partial x)(x^8y^5+4x^6y) ?

The answer to (\partial)/(\partial x)(x^8y^5+4x^6y) is 8y^5x^7+24yx^5

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(\partial)/(\partial x)(x^8y^5+4x^6y)

\frac{\partial}{\partial x} (x^{8} y^{5} + 4 x^{6} y)

8 y^{5} x^{7} + 24 y x^{5}

Solution steps

\frac{\partial}{\partial x} (x^{8} y^{5} + 4 x^{6} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{8} y^{5}) + \frac{\partial}{\partial x} (4 x^{6} y)

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

\frac{\partial}{\partial x} (4 x^{6} y) = 24 y x^{5}

= 8 y^{5} x^{7} + 24 y x^{5}

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

\int x (x - 5)^{5} d x

(4 x - 7)^{3} (8 x - 3)

x \to 0 lim (\frac{x ^{5} + 6 x}{x})

n = 0 \sum \infty (- \frac{2}{3})^{n}

What is (\partial)/(\partial x)(x^8y^5+4x^6y) ?
The answer to (\partial)/(\partial x)(x^8y^5+4x^6y) is 8y^5x^7+24yx^5