What is implicit x^5+y^5=10 ?

The answer to implicit x^5+y^5=10 is (dy)/(dx)=-(x^4)/(y^4)

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implicit x^5+y^5=10

implicit derivative

x^{5} + y^{5} = 10

\frac{d y}{d x} = - \frac{x ^{4}}{y ^{4}}

Solution steps

x^{5} + y^{5} = 10

Treat

y

y (x)

Differentiate both sides:

5 x^{4} + 5 y^{4} \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{x ^{4}}{y ^{4}}

\frac{d y}{d x} = - \frac{x ^{4}}{y ^{4}}

What is implicit x^5+y^5=10 ?
The answer to implicit x^5+y^5=10 is (dy)/(dx)=-(x^4)/(y^4)