What is the derivative of (3x-1/(sqrt(x))) ?

The derivative of (3x-1/(sqrt(x))) is (3x+1)/(2xsqrt(x))

What is the first derivative of (3x-1/(sqrt(x))) ?

The first derivative of (3x-1/(sqrt(x))) is (3x+1)/(2xsqrt(x))

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

\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}

\frac{\partial}{\partial x} (2 x^{2} + 3 y^{2})

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

\int_{0}^{16} sin (x) d x

\int sin^{n} (x) d x

\frac{d}{d x} (x^{9 s i n (x)})

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