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

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

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

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

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derivative of

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

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

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int \frac{28}{28 + e ^{x}} d x

2 x \frac{d y}{d x} + y = 6 x

x \to 3 + lim (6 + x)

y = \frac{6}{x ^{2}}, (1, 6)

\int \frac{1}{x ^{2} ( x ^{2} - 9 )} d x

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