What is the derivative of y= 2/((4x-3)^{1/2)} ?

The derivative of y= 2/((4x-3)^{1/2)} is -4/((4x-3)^{3/2)}

What is the first derivative of y= 2/((4x-3)^{1/2)} ?

The first derivative of y= 2/((4x-3)^{1/2)} is -4/((4x-3)^{3/2)}

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derivative of

y = \frac{2}{( 4 x - 3 ) ^{\frac{1}{2}}}

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (4 x - 3) = 4

= 2 (- \frac{1}{2 ( 4 x - 3 ) ^{\frac{3}{2}}} \cdot 4)

Simplify

2 (- \frac{1}{2 ( 4 x - 3 ) ^{\frac{3}{2}}} \cdot 4) : - \frac{4}{( 4 x - 3 ) ^{\frac{3}{2}}}

= - \frac{4}{( 4 x - 3 ) ^{\frac{3}{2}}}

f (x) = (1 + 2 x)^{2}

(4 x + 5)^{3}

x \to \frac{π}{2} lim (- cot (2 x))

\frac{d}{d x} (12 tan (cosh (e^{4 x})))

\int (e^{- x} - e^{3}) (e^{x} - e^{- 5}) d x

What is the derivative of y= 2/((4x-3)^{1/2)} ?
The derivative of y= 2/((4x-3)^{1/2)} is -4/((4x-3)^{3/2)}
What is the first derivative of y= 2/((4x-3)^{1/2)} ?
The first derivative of y= 2/((4x-3)^{1/2)} is -4/((4x-3)^{3/2)}