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Popular >

derivative of (4x-3^{1/2})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches-2 of-x^3+x

x \to - 2 lim (- x^{3} + x)

tangent of f(x)= x/((1+x^2)),\at x=3 tangent of

f (x) = \frac{x}{( 1 + x ^{2} )}, at x = 3

integral from-3 to-1 of (x^2-4x+8)

\int_{- 3}^{- 1} (x^{2} - 4 x + 8) d x

limit as x approaches-1 of 3^{2x}

x \to - 1 lim (3^{2 x})

derivative of (x^2/(x^2-4))

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

Frequently Asked Questions (FAQ)

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