What is the derivative of 1/(3x-1) ?

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

What is the first derivative of 1/(3x-1) ?

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

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derivative of

\frac{1}{3 x - 1}

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

Solution steps

\frac{d}{d x} (\frac{1}{3 x - 1})

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} + y = x, y (0) = 4

\int \frac{10 x}{2 + 5 x ^{2}} d x

x \to - 1 lim (\frac{x + 1}{x - 1})

y = x^{3} + 1, (1, 2)

f (x) = \frac{1}{x ^{4}}

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