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

The derivative of 2/((x+2^3)) is -6/((x+2)^4)

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

The first derivative of 2/((x+2^3)) is -6/((x+2)^4)

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

- \frac{6}{( x + 2 ) ^{4}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 (- \frac{3}{( x + 2 ) ^{4}} \cdot 1) : - \frac{6}{( x + 2 ) ^{4}}

= - \frac{6}{( x + 2 ) ^{4}}

\frac{\partial}{\partial x} (7 - x^{2} + x y - 2 y^{2})

\frac{d}{d x} (6 x^{- 2})

4 x - x^{2}, (1.3)

f (x) = 5 x^{4} - 6 x^{2} + 1

\frac{\partial}{\partial x} (2 x y - 3)

What is the derivative of 2/((x+2^3)) ?
The derivative of 2/((x+2^3)) is -6/((x+2)^4)
What is the first derivative of 2/((x+2^3)) ?
The first derivative of 2/((x+2^3)) is -6/((x+2)^4)