What is the derivative of 3/((x+2^2)) ?

The derivative of 3/((x+2^2)) is -6/((x+2)^3)

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

The first derivative of 3/((x+2^2)) is -6/((x+2)^3)

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

- \frac{6}{( x + 2 ) ^{3}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (\frac{1}{( x + 2 ) ^{2}})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

3 (- \frac{2}{( x + 2 ) ^{3}} \cdot 1) : - \frac{6}{( x + 2 ) ^{3}}

= - \frac{6}{( x + 2 ) ^{3}}

y^{^{'}} = e^{4 x} - 3 x

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

y^{^{'}} = x^{2} - y

36 y^{^{''}} - y = x e^{\frac{x}{6}}, y (0) = 1, y^{^{'}} (0) = 0

f^{^{'}} (x) = 1

What is the derivative of 3/((x+2^2)) ?
The derivative of 3/((x+2^2)) is -6/((x+2)^3)
What is the first derivative of 3/((x+2^2)) ?
The first derivative of 3/((x+2^2)) is -6/((x+2)^3)