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

The derivative of 2/((3x^2)) is -4/(9x^3)

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

The first derivative of 2/((3x^2)) is -4/(9x^3)

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

- \frac{4}{9 x ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

2 (- \frac{2}{( 3 x ) ^{3}} \cdot 3) : - \frac{4}{9 x ^{3}}

= - \frac{4}{9 x ^{3}}

x \to 0.1 lim (\frac{5 sin ( x )}{x})

x \to 6 lim (\frac{x ^{2} - 3 x - 18}{x - 6})

(- 3.2) (6.3)

\int_{\frac{π}{4}}^{π} sin (2 x) d x

e^{\frac{7}{x}}

What is the derivative of 2/((3x^2)) ?
The derivative of 2/((3x^2)) is -4/(9x^3)
What is the first derivative of 2/((3x^2)) ?
The first derivative of 2/((3x^2)) is -4/(9x^3)