Question

Qual a derivada implícita de x^4*y+y-6x^2=7

Answer 1

Só terá que aplicar a notação dy/dx quando derivar um termo que contenha a incógnita y.

$x^{4}y+y-6x^{2}=7 \\ \\ \\ (x^{4}'y+x^{4}y')+1 \cdot \, \displaystyle \frac{dy}{dx}-12x=0 \\ \\ \\ 4x^{3}y+x^{4} \cdot 1 \cdot \, \displaystyle \frac{dy}{dx}+ 1 \cdot \displaystyle \frac{dy}{dx}-12x=0 \\ \\ \\ 4x^{3}y+x^{4} \, \displaystyle \frac{dy}{dx}+\displaystyle \frac{dy}{dx}-12x=0 \\ \\ \\ \displaystyle \frac{dy}{dx}(x^4}+1)=12x-4x^{3}y \\ \\ \\ \boxed{\boxed{\displaystyle \frac{dy}{dx}= \frac{12x-4x^{3}y}{x^{4}+1}}}$