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))

(\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}}

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

x \to - \infty lim (x 2)

t an g e n t f (x) = x^{2} + 9, (- 4, 25)

\int 10 e^{- 10 x} d x

\int - \frac{8}{π} x d 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))