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Popular >

derivative of (4x+1)/(sqrt(x))

Solution

derivative of

\frac{4 x + 1}{x}

Solution

\frac{4 x - 1}{2 x x}

Solution steps

\frac{d}{d x} (\frac{4 x + 1}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (4 x + 1) = 4

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

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

Simplify

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

= \frac{4 x - 1}{2 x x}

Popular Examples

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\frac{d y}{d x} = \frac{x}{1 + x ^{2}}

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Frequently Asked Questions (FAQ)

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