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

The derivative of 1/(x(x+2^2)) is -(3x+2)/(x^2(x+2)^3)

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

The first derivative of 1/(x(x+2^2)) is -(3x+2)/(x^2(x+2)^3)

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(tan (2 x))^{^{'}}

(\frac{4 x ^{3}}{3} + 2 x + cos (x) + 1)^{^{'}}

\int (16 - 4 x^{2}) d x

\frac{d}{d x} (2 - sin (x))

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

What is the derivative of 1/(x(x+2^2)) ?
The derivative of 1/(x(x+2^2)) is -(3x+2)/(x^2(x+2)^3)
What is the first derivative of 1/(x(x+2^2)) ?
The first derivative of 1/(x(x+2^2)) is -(3x+2)/(x^2(x+2)^3)