What is the derivative of 3/((8x+3^2)) ?

The derivative of 3/((8x+3^2)) is -(48)/((8x+3)^3)

What is the first derivative of 3/((8x+3^2)) ?

The first derivative of 3/((8x+3^2)) is -(48)/((8x+3)^3)

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

- \frac{48}{( 8 x + 3 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

3 (- \frac{2}{( 8 x + 3 ) ^{3}} \cdot 8) : - \frac{48}{( 8 x + 3 ) ^{3}}

= - \frac{48}{( 8 x + 3 ) ^{3}}

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What is the derivative of 3/((8x+3^2)) ?
The derivative of 3/((8x+3^2)) is -(48)/((8x+3)^3)
What is the first derivative of 3/((8x+3^2)) ?
The first derivative of 3/((8x+3^2)) is -(48)/((8x+3)^3)