Answer:
[tex]\frac{dy}{dx} = - \frac{2\cdot x \cdot y}{(x^{2}+y^{4}+5)\cdot \ln(x^{2}+y^{4}+5)+4\cdot y^{4}}[/tex]
Step-by-step explanation:
The implicite derivative of the function is:
[tex]\frac{dy}{dx}\cdot \ln (x^{2}+y^{4}+5) + \frac{y}{(x^{2}+y^{4}+5)}\cdot (2\cdot x + 4\cdot y^{3}\cdot \frac{dy}{dx} )=0[/tex]
[tex]\frac{dy}{dx}\cdot(x^{2}+y^{4}+5)\cdot \ln (x^{2}+y^{4}+5)+y\cdot (2\cdot x+4\cdot y^{3}\cdot \frac{dy}{dx} )= 0[/tex]
[tex][(x^{2}+y^{4}+5)\cdot \ln(x^{2}+y^{4}+5)+4\cdot y^{4}]\cdot \frac{dy}{dx} + 2\cdot x \cdot y = 0[/tex]
[tex]\frac{dy}{dx} = - \frac{2\cdot x \cdot y}{(x^{2}+y^{4}+5)\cdot \ln(x^{2}+y^{4}+5)+4\cdot y^{4}}[/tex]
