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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\frac{d}{d x} (\frac{375}{x ^{4}})

\int \frac{tan ^{3} ( x )}{cos ^{2} ( x )} d x

\int - 3 e^{- x} d x

\int (x^{2} - 4)^{4} (2 x) d x

\int \frac{x ^{2}}{( x ^{3} - 1 ) ^{4}} d x

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