What is the derivative of (1-2x/(3x^2)) ?

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

What is the first derivative of (1-2x/(3x^2)) ?

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x \to 1 lim (\frac{2}{x ^{3} - x})

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

\frac{d ^{2}}{d x ^{2}} (e^{\frac{6}{x}})

x \to \infty lim (- 3 x^{3} + x)

y = 0, y = 3 (x^{3} - x)

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