What is the derivative of (5x+1/(2sqrt(x))) ?

The derivative of (5x+1/(2sqrt(x))) is (5x-1)/(4xsqrt(x))

What is the first derivative of (5x+1/(2sqrt(x))) ?

The first derivative of (5x+1/(2sqrt(x))) is (5x-1)/(4xsqrt(x))

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\frac{d}{d x} (\frac{5 x + 1}{2 x})

\frac{5 x - 1}{4 x x}

Solution steps

\frac{d}{d x} (\frac{5 x + 1}{2 x})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{5 x + 1}{x})

Apply the Quotient Rule:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( 5 x + 1 ) x - \frac{d}{d x} ( x ) ( 5 x + 1 )}{( x ) ^{2}}

\frac{d}{d x} (5 x + 1) = 5

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

= \frac{1}{2} \cdot \frac{5 x - \frac{1}{2 x} ( 5 x + 1 )}{( x ) ^{2}}

Simplify

\frac{1}{2} \cdot \frac{5 x - \frac{1}{2 x} ( 5 x + 1 )}{( x ) ^{2}} : \frac{5 x - 1}{4 x x}

= \frac{5 x - 1}{4 x x}

What is the derivative of (5x+1/(2sqrt(x))) ?
The derivative of (5x+1/(2sqrt(x))) is (5x-1)/(4xsqrt(x))
What is the first derivative of (5x+1/(2sqrt(x))) ?
The first derivative of (5x+1/(2sqrt(x))) is (5x-1)/(4xsqrt(x))