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Popular >

derivative of f(x)=(x+3)/(sqrt(x))

Solution

derivative of

f (x) = \frac{x + 3}{x}

Solution

\frac{x - 3}{2 x x}

Solution steps

\frac{d}{d x} (\frac{x + 3}{x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{x - 3}{2 x x}

Popular Examples

derivative of (a+bx+cx^2/x)

\frac{d}{d x} (\frac{a + b x + c x ^{2}}{x})

tangent of f(x)=sqrt(x-1),(17,4)tangent of

f (x) = x - 1, (17, 4)

sum from n=0 to infinity of 4-sin(n)

n = 0 \sum \infty 4 - sin (n)

integral from 0 to 2 of 1/(e^{pix)}

\int_{0}^{2} \frac{1}{e ^{π x}} d x

(dy)/(dx)+4y=e^{-4x}

\frac{d y}{d x} + 4 y = e^{- 4 x}

Frequently Asked Questions (FAQ)

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