What is the derivative of (9+x)^2((100)/(x^2)+1) ?

The derivative of (9+x)^2((100)/(x^2)+1) is 2x-(16200)/(x^3)-(1800)/(x^2)+18

What is the first derivative of (9+x)^2((100)/(x^2)+1) ?

The first derivative of (9+x)^2((100)/(x^2)+1) is 2x-(16200)/(x^3)-(1800)/(x^2)+18

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derivative of

(9 + x)^{2} (\frac{100}{x ^{2}} + 1)

2 x - \frac{16200}{x ^{3}} - \frac{1800}{x ^{2}} + 18

Solution steps

\frac{d}{d x} ((9 + x)^{2} (\frac{100}{x ^{2}} + 1))

Simplify

(9 + x)^{2} (\frac{100}{x ^{2}} + 1) : x^{2} + 18 x + \frac{8100}{x ^{2}} + \frac{1800}{x} + 181

= \frac{d}{d x} (x^{2} + 18 x + \frac{8100}{x ^{2}} + \frac{1800}{x} + 181)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{2}) + \frac{d}{d x} (18 x) + \frac{d}{d x} (\frac{8100}{x ^{2}}) + \frac{d}{d x} (\frac{1800}{x}) + \frac{d}{d x} (181)

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

\frac{d}{d x} (18 x) = 18

\frac{d}{d x} (\frac{8100}{x ^{2}}) = - \frac{16200}{x ^{3}}

\frac{d}{d x} (\frac{1800}{x}) = - \frac{1800}{x ^{2}}

\frac{d}{d x} (181) = 0

= 2 x + 18 - \frac{16200}{x ^{3}} - \frac{1800}{x ^{2}} + 0

Simplify

= 2 x - \frac{16200}{x ^{3}} - \frac{1800}{x ^{2}} + 18

\int e^{- l n (x)} (1 - \frac{1}{x}) d x

9 e^{x} + x

\frac{d}{d x} (ln (\frac{x - 1}{x + 1}))

(x^{2} + 1) \frac{d y}{d x} + 2 x y - x = 0

What is the derivative of (9+x)^2((100)/(x^2)+1) ?
The derivative of (9+x)^2((100)/(x^2)+1) is 2x-(16200)/(x^3)-(1800)/(x^2)+18
What is the first derivative of (9+x)^2((100)/(x^2)+1) ?
The first derivative of (9+x)^2((100)/(x^2)+1) is 2x-(16200)/(x^3)-(1800)/(x^2)+18