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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 x ^{2} + 4 x y + y ^{6}} \frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6})

= \frac{1}{2 x ^{2} + 4 x y + y ^{6}} \frac{\partial}{\partial x} (x^{2} + 4 x y + y^{6})

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

= \frac{1}{2 x ^{2} + 4 x y + y ^{6}} (2 x + 4 y)

Simplify

\frac{1}{2 x ^{2} + 4 x y + y ^{6}} (2 x + 4 y) : \frac{x + 2 y}{x ^{2} + 4 x y + y ^{6}}

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

\frac{d}{d x} (\frac{x}{2 ^{x}})

\int_{1}^{e} x^{n} ln (x^{m}) d x

\frac{d ^{2}}{d x ^{2}} (e^{6 e^{x}})

f (x) = x^{4} - 4 x^{3} - 20 x^{2} + 96 x + 60

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 2

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