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}}

x \to 0 - lim (\frac{1}{13 x})

f (x) = \frac{4 ( x ^{2} - 1 )}{( 4 x ^{3} - 2 x ) ^{\frac{2}{3}}}

\int t e^{- t^{2}} d t

x \to - \frac{π}{9} lim (9 x^{2} (5 x))

ln (8 - t^{2})

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