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Popular Calculus >

derivative of (3x-8)/(sqrt(x))

Solution

derivative of

\frac{3 x - 8}{x}

Solution

\frac{3 x + 8}{2 x x}

Solution steps

\frac{d}{d x} (\frac{3 x - 8}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 x - 8 ) x - \frac{d}{d x} ( x ) ( 3 x - 8 )}{( x ) ^{2}}

\frac{d}{d x} (3 x - 8) = 3

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

= \frac{3 x - \frac{1}{2 x} ( 3 x - 8 )}{( x ) ^{2}}

Simplify

\frac{3 x - \frac{1}{2 x} ( 3 x - 8 )}{( x ) ^{2}} : \frac{3 x + 8}{2 x x}

= \frac{3 x + 8}{2 x x}

Graph

Popular Examples

derivative of (e^x+e^{-x}/2)

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{2})

y^{''}-10y^'+25y=0,y(0)=-3,y^'(0)=-29/2

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = - \frac{29}{2}

derivative of f(x)=-(13)/(x^4)

d er i v a t i v e f (x) = - \frac{13}{x ^{4}}

integral of ((2x+3))/((x+1)^2)

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

tangent of 110x-16x^2

t an g e n t 110 x - 16 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of (3x-8)/(sqrt(x)) ?
The derivative of (3x-8)/(sqrt(x)) is (3x+8)/(2xsqrt(x))
What is the first derivative of (3x-8)/(sqrt(x)) ?
The first derivative of (3x-8)/(sqrt(x)) is (3x+8)/(2xsqrt(x))