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Popular >

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

Solution

derivative of

y = \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

derivative of-(5e^{5/x})/(x^2)derivative of

- \frac{5 e ^{\frac{5}{x}}}{x ^{2}}

laplacetransform 200e^{-2t}+100e^{-t}+10 laplace transform

200 e^{- 2 t} + 100 e^{- t} + 10

(dy)/(dx)+2xy=x

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

limit as x approaches 1 of sqrt(x-2)

x \to 1 lim (x - 2)

d/(dy)(e^xcos(xy))

\frac{d}{d y} (e^{x} cos (x y))

Frequently Asked Questions (FAQ)

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