Find the derivative of -3y+2x+y^3=0

\frac{d}{dx}\left(y^3-3y+2x=0\right)

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Answer

$false$

Step by step solution

Problem

$\frac{d}{dx}\left(y^3-3y+2x=0\right)$
1

Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

$\frac{d}{dx}\left(2x-3y+y^3\right)=\frac{d}{dx}\left(0\right)$
2

The derivative of the constant function is equal to zero

$\frac{d}{dx}\left(2x-3y+y^3\right)=0$
3

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(2x\right)+\frac{d}{dx}\left(-3y\right)+\frac{d}{dx}\left(y^3\right)=0$
4

The derivative of the constant function is equal to zero

$\frac{d}{dx}\left(2x\right)+0+0=0$
5

The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function

$2\frac{d}{dx}\left(x\right)+0+0=0$
6

The derivative of the linear function is equal to $1$

$1\cdot 2+0+0=0$
7

Add the values $0$ and $0$

$2=0$
8

$2$ not equal to $0$

$false$

Answer

$false$

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Problem Analysis

Main topic:

Differential calculus

Time to solve it:

0.2 seconds

Views:

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