What is (\partial)/(\partial x)(sqrt(x^2+4xy+y^6)-8) ?

The answer to (\partial)/(\partial x)(sqrt(x^2+4xy+y^6)-8) is (x+2y)/(sqrt(x^2+4xy+y^6))

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(\partial)/(\partial x)(sqrt(x^2+4xy+y^6)-8)

\frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6} - 8)

\frac{x + 2 y}{x ^{2} + 4 x y + y ^{6}}

Solution steps

\frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6} - 8)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6}) - \frac{\partial}{\partial x} (8)

\frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6}) = \frac{x + 2 y}{x ^{2} + 4 y x + y ^{6}}

\frac{\partial}{\partial x} (8) = 0

= \frac{x + 2 y}{x ^{2} + 4 y x + y ^{6}} - 0

Simplify

= \frac{x + 2 y}{x ^{2} + 4 x y + y ^{6}}

\frac{d}{d x} (4 x^{2} e^{2 x^{2} + x - 1})

x \to - 3 lim (3 x^{2} + 5 x + 1)

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

\int_{- a}^{a} a^{2} - x^{2} d x

x \to 1 lim (\frac{x ^{2} - 5}{x})

What is (\partial)/(\partial x)(sqrt(x^2+4xy+y^6)-8) ?
The answer to (\partial)/(\partial x)(sqrt(x^2+4xy+y^6)-8) is (x+2y)/(sqrt(x^2+4xy+y^6))