What is derivative of x^5+y^4=500 ?

The answer to derivative of x^5+y^4=500 is (dy)/(dx)=-(5x^4)/(4y^3)

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derivative of x^5+y^4=500

derivative of

x^{5} + y^{4} = 500

\frac{d y}{d x} = - \frac{5 x ^{4}}{4 y ^{3}}

Solution steps

x^{5} + y^{4} = 500

Treat

y

y (x)

Differentiate both sides:

5 x^{4} + 4 y^{3} \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{5 x ^{4}}{4 y ^{3}}

\frac{d y}{d x} = - \frac{5 x ^{4}}{4 y ^{3}}

s = \frac{1}{t}

x^{2} + y^{2} x + 6 x = 1

x = \frac{y ^{3}}{3 + y}

x^{2} + y^{2} = 2 x y

v = 2 - 4 t - 6 t^{3}

What is derivative of x^5+y^4=500 ?
The answer to derivative of x^5+y^4=500 is (dy)/(dx)=-(5x^4)/(4y^3)