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# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\frac{d}{dx}\left(y=\frac{3}{x}-\frac{2}{x^2}+\frac{2}{3x^3}\right)$

Learn how to solve implicit differentiation problems step by step online.

$\frac{d}{dx}\left(y=\frac{3}{x}+\frac{-2}{x^2}+\frac{\frac{2}{3}}{x^3}\right)$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)(y=3/x-2/(x^2)+2/(3x^3)). Divide 2 by 3. Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function is equal to 1. The derivative of a sum of two functions is the sum of the derivatives of each function.

$y^{\prime}=\frac{-3}{x^2}+\frac{4}{x^{3}}+\frac{-2}{x^{4}}$

### Problem Analysis

$\frac{d}{dx}\left(y=\frac{3}{x}-\frac{2}{x^2}+\frac{2}{3x^3}\right)$

### Main topic:

Implicit differentiation

~ 0.12 seconds