Question

Derivada implícita de
$(2x-1)^4+10=y^2+20$

Answer 1

Boa tarde.

Acredito que a derivação implícita seja dy/dx.

Temos que 

$4(2x-1)^3 . (2) = 2y \displaystyle\frac{dx}{dy} \Rightarrow \displaystyle\frac{dx}{dy} = \displaystyle\frac{8(2x-1)^3}{2y} \Rightarrow \displaystyle\frac{dx}{dy}=\displaystyle\frac{4(2x-1)^3}{y}$

Espero ter ajudado. 

Answer 2

$\\ (2x-1)^4 +10 = y^2+20 \\ \\ -y^2= -(2x-1)^4+20-10 \\ \\ -2y^2^-^1 \frac{dx}{dy} = -4(2x-1)^4^-^1*(2x)' + 0 \\ \\ -2y \frac{dx}{dy} = -4(2x-1)^3*2 \\ \\ -2y \frac{dx}{dy} = -8(2x-1)^3 \\ \\ \frac{dx}{dy} = \frac{-8(2x-1)^3}{-2y} \\ \\ \frac{dx}{dy} = \frac{4(2x-1)^3}{y}$