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Popular >

derivative of f(x)=(3x-1)/(sqrt(x))

Solution

derivative of

f (x) = \frac{3 x - 1}{x}

Solution

\frac{3 x + 1}{2 x x}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{3 x + 1}{2 x x}

Popular Examples

integral of (cos^5(x))/(sin^3(x))

\int \frac{cos ^{5} ( x )}{sin ^{3} ( x )} d x

integral from 0 to 0.6 of 1/((1-x)(3-x))

\int_{0}^{0.6} \frac{1}{( 1 - x ) ( 3 - x )} d x

integral of 1/(t^2sqrt(2-t^2))

\int \frac{1}{t ^{2} 2 - t ^{2}} d t

derivative of ((cos(x)))/(cos^2(*x)-1)derivative of

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

integral of (n+3)3

\int (n + 3) 3 d n

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(3x-1)/(sqrt(x)) ?
The derivative of f(x)=(3x-1)/(sqrt(x)) is (3x+1)/(2xsqrt(x))
What is the first derivative of f(x)=(3x-1)/(sqrt(x)) ?
The first derivative of f(x)=(3x-1)/(sqrt(x)) is (3x+1)/(2xsqrt(x))