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

The answer to (\partial)/(\partial x)(x^5+7x^5y) is 5x^4+35yx^4

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

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

5 x^{4} + 35 y x^{4}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (7 x^{5} y) = 35 y x^{4}

= 5 x^{4} + 35 y x^{4}

x \to - 4 lim (\frac{x ^{2} + 3}{x - 1})

e^{y} y^{^{'}} + \frac{t}{y + 1} = \frac{2}{y + 1}

x \to \infty lim (\frac{1}{6 ^{x + 1}})

(6, 2), (- 3, 5)

\frac{2 x - 3}{4 x + 1}

What is (\partial)/(\partial x)(x^5+7x^5y) ?
The answer to (\partial)/(\partial x)(x^5+7x^5y) is 5x^4+35yx^4