What is the derivative of 2/(5x-1) ?

The derivative of 2/(5x-1) is -(10)/((5x-1)^2)

What is the first derivative of 2/(5x-1) ?

The first derivative of 2/(5x-1) is -(10)/((5x-1)^2)

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\frac{d}{d x} (\frac{2}{5 x - 1})

- \frac{10}{( 5 x - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2}{5 x - 1})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{1}{5 x - 1})

Apply exponent rule:

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

= 2 \frac{d}{d x} ((5 x - 1)^{- 1})

Apply the chain rule:

- \frac{1}{( 5 x - 1 ) ^{2}} \frac{d}{d x} (5 x - 1)

= - \frac{1}{( 5 x - 1 ) ^{2}} \frac{d}{d x} (5 x - 1)

\frac{d}{d x} (5 x - 1) = 5

= 2 (- \frac{1}{( 5 x - 1 ) ^{2}} \cdot 5)

Simplify

2 (- \frac{1}{( 5 x - 1 ) ^{2}} \cdot 5) : - \frac{10}{( 5 x - 1 ) ^{2}}

= - \frac{10}{( 5 x - 1 ) ^{2}}

\frac{4}{s}

\int (x + 5)^{9} d x

\int x^{2} 5 x + 4 d x

f (x) = x^{3} - 6 x^{2} + 8, g (x) = x^{2} - 4 x

\frac{d y}{d x} = (x - 8) e^{- 2 y}

What is the derivative of 2/(5x-1) ?
The derivative of 2/(5x-1) is -(10)/((5x-1)^2)
What is the first derivative of 2/(5x-1) ?
The first derivative of 2/(5x-1) is -(10)/((5x-1)^2)