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\frac{d}{dx}\left(x^3y+y^3x=30\right)

Derive the function x^3y+y^3x=30 with respect to x

Answer

$y^3+3y\cdot x^{2}=0$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(x^3y+y^3x=30\right)$
1

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

$\frac{d}{dx}\left(x\cdot y^3+y\cdot x^3\right)=\frac{d}{dx}\left(30\right)$

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Answer

$y^3+3y\cdot x^{2}=0$

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$\frac{d}{dx}\left(x^3y+y^3x=30\right)$

Main topic:

Differential calculus

Used formulas:

5. See formulas

Time to solve it:

~ 0.25 seconds