What is the derivative of-9/((1+3x^2)) ?

The derivative of-9/((1+3x^2)) is (54)/((1+3x)^3)

What is the first derivative of-9/((1+3x^2)) ?

The first derivative of-9/((1+3x^2)) is (54)/((1+3x)^3)

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\frac{d}{d x} (- \frac{9}{( 1 + 3 x ) ^{2}})

\frac{54}{( 1 + 3 x ) ^{3}}

Solution steps

\frac{d}{d x} (- \frac{9}{( 1 + 3 x ) ^{2}})

Take the constant out:

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

= - 9 \frac{d}{d x} (\frac{1}{( 1 + 3 x ) ^{2}})

Apply exponent rule:

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

= - 9 \frac{d}{d x} ((1 + 3 x)^{- 2})

Apply the chain rule:

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

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

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

= - 9 (- \frac{2}{( 1 + 3 x ) ^{3}} \cdot 3)

Simplify

- 9 (- \frac{2}{( 1 + 3 x ) ^{3}} \cdot 3) : \frac{54}{( 1 + 3 x ) ^{3}}

= \frac{54}{( 1 + 3 x ) ^{3}}

What is the derivative of-9/((1+3x^2)) ?
The derivative of-9/((1+3x^2)) is (54)/((1+3x)^3)
What is the first derivative of-9/((1+3x^2)) ?
The first derivative of-9/((1+3x^2)) is (54)/((1+3x)^3)