What is the derivative of sqrt((4+8/x ^2+(2+x)^2)) ?

The derivative of sqrt((4+8/x ^2+(2+x)^2)) is (x^3-32)/(x^2sqrt(x^2+16))

What is the first derivative of sqrt((4+8/x ^2+(2+x)^2)) ?

The first derivative of sqrt((4+8/x ^2+(2+x)^2)) is (x^3-32)/(x^2sqrt(x^2+16))

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\frac{d}{d x} (4 + \frac{8}{x})^{2} + (2 + x)^{2}

\frac{x ^{3} - 32}{x ^{2} x ^{2} + 16}

Solution steps

\frac{d}{d x} (4 + \frac{8}{x})^{2} + (2 + x)^{2}

Apply the chain rule:

\frac{1}{2 ( 4 + \frac{8}{x} ) ^{2} + ( 2 + x ) ^{2}} \frac{d}{d x} ((4 + \frac{8}{x})^{2} + (2 + x)^{2})

= \frac{1}{2 ( 4 + \frac{8}{x} ) ^{2} + ( 2 + x ) ^{2}} \frac{d}{d x} ((4 + \frac{8}{x})^{2} + (2 + x)^{2})

\frac{d}{d x} ((4 + \frac{8}{x})^{2} + (2 + x)^{2}) = 2 x - \frac{64}{x ^{2}} - \frac{128}{x ^{3}} + 4

= \frac{1}{2 ( 4 + \frac{8}{x} ) ^{2} + ( 2 + x ) ^{2}} (2 x - \frac{64}{x ^{2}} - \frac{128}{x ^{3}} + 4)

Simplify

\frac{1}{2 ( 4 + \frac{8}{x} ) ^{2} + ( 2 + x ) ^{2}} (2 x - \frac{64}{x ^{2}} - \frac{128}{x ^{3}} + 4) : \frac{x ^{3} - 32}{x ^{2} x ^{2} + 16}

= \frac{x ^{3} - 32}{x ^{2} x ^{2} + 16}

y = x^{2} - 1, x = 1, x = 3

\int 3 x ln (4 x) d x

f (x) = (3 - 5 x)^{9}

\frac{d}{d x} (cos^{2} ((a - x)^{3}))

What is the derivative of sqrt((4+8/x ^2+(2+x)^2)) ?
The derivative of sqrt((4+8/x ^2+(2+x)^2)) is (x^3-32)/(x^2sqrt(x^2+16))
What is the first derivative of sqrt((4+8/x ^2+(2+x)^2)) ?
The first derivative of sqrt((4+8/x ^2+(2+x)^2)) is (x^3-32)/(x^2sqrt(x^2+16))