What is the derivative of f(x)= 1/(3x^2) ?

The derivative of f(x)= 1/(3x^2) is -2/(3x^3)

What is the first derivative of f(x)= 1/(3x^2) ?

The first derivative of f(x)= 1/(3x^2) is -2/(3x^3)

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derivative of

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

- \frac{2}{3 x ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

= - \frac{2}{3 x ^{3}}

y - 3 = 5 (x - 2)

f (x) = x + \frac{1}{x}

(- \frac{17}{8}, - \frac{19}{6}), (\frac{25}{6}, \frac{3}{2})

(0, - 10)

y = - 2 x + 5

What is the derivative of f(x)= 1/(3x^2) ?
The derivative of f(x)= 1/(3x^2) is -2/(3x^3)
What is the first derivative of f(x)= 1/(3x^2) ?
The first derivative of f(x)= 1/(3x^2) is -2/(3x^3)