What is derivative of x^4+y^4=4a^2x^3y^3 ?

The answer to derivative of x^4+y^4=4a^2x^3y^3 is (dy)/(dx)=(x^2(3a^2y^3-x))/(y^2(y-3a^2x^3))

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derivative of x^4+y^4=4a^2x^3y^3

derivative of

x^{4} + y^{4} = 4 a^{2} x^{3} y^{3}

\frac{d y}{d x} = \frac{x ^{2} ( 3 a ^{2} y ^{3} - x )}{y ^{2} ( y - 3 a ^{2} x ^{3} )}

Solution steps

x^{4} + y^{4} = 4 a^{2} x^{3} y^{3}

Treat

y

y (x)

Differentiate both sides:

4 x^{3} + 4 y^{3} \frac{d y}{d x} = 4 a^{2} (3 x^{2} y^{3} + 3 y^{2} \frac{d y}{d x} x^{3})

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{x ^{2} ( 3 a ^{2} y ^{3} - x )}{y ^{2} ( y - 3 a ^{2} x ^{3} )}

\frac{d y}{d x} = \frac{x ^{2} ( 3 a ^{2} y ^{3} - x )}{y ^{2} ( y - 3 a ^{2} x ^{3} )}

(d^{2} + d) \cdot y = x^{2} + 2 x + 4

(d^{2} + d) y = x^{2} + 2 x + 4

x = e^{s i n (t^{2} - 4 t)}

(d^{2} + 1) \cdot y = x^{2} \cdot (cos (x))

x^{3} + y^{3} = 9

What is derivative of x^4+y^4=4a^2x^3y^3 ?
The answer to derivative of x^4+y^4=4a^2x^3y^3 is (dy)/(dx)=(x^2(3a^2y^3-x))/(y^2(y-3a^2x^3))