What is (\partial)/(\partial x)(8y^5+8y^2x^7) ?

The answer to (\partial)/(\partial x)(8y^5+8y^2x^7) is 56y^2x^6

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(\partial)/(\partial x)(8y^5+8y^2x^7)

\frac{\partial}{\partial x} (8 y^{5} + 8 y^{2} x^{7})

56 y^{2} x^{6}

Solution steps

\frac{\partial}{\partial x} (8 y^{5} + 8 y^{2} x^{7})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (8 y^{5}) + \frac{\partial}{\partial x} (8 y^{2} x^{7})

\frac{\partial}{\partial x} (8 y^{5}) = 0

\frac{\partial}{\partial x} (8 y^{2} x^{7}) = 56 y^{2} x^{6}

= 0 + 56 y^{2} x^{6}

Simplify

= 56 y^{2} x^{6}

\frac{d}{d x} (\frac{20}{x + 1})

x \to + 0 lim (\frac{7}{x} - \frac{7}{x ^{2} - x})

x \to 0 lim (2 - \frac{1}{x ^{3}})

x \to 0 lim (2 - x)

x \to 5 lim (2 x + 1)

What is (\partial)/(\partial x)(8y^5+8y^2x^7) ?
The answer to (\partial)/(\partial x)(8y^5+8y^2x^7) is 56y^2x^6