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

The derivative of sqrt(1+1/(3x)) is -1/(2sqrt(3)x^{3/2)sqrt(3x+1)}

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

The first derivative of sqrt(1+1/(3x)) is -1/(2sqrt(3)x^{3/2)sqrt(3x+1)}

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

- \frac{1}{2 3 x ^{\frac{3}{2}} 3 x + 1}

Solution steps

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

Apply the chain rule:

\frac{1}{2 1 + \frac{1}{3 x}} \frac{d}{d x} (1 + \frac{1}{3 x})

= \frac{1}{2 1 + \frac{1}{3 x}} \frac{d}{d x} (1 + \frac{1}{3 x})

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

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

Simplify

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

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

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

11 + tan^{2} (x)

n = 0 \sum \infty p (1 - p)^{n}

e^{- x^{2}} cos (x)

\int e^{2 x} \cdot sin (3 x) d x

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