4. Applications of Derivatives

Find $dy/dx$ for the equation below using implicit differentiation.

$3\(\sqrt{y}\)=x-y$

Find $dy/dx$ for the equation below using implicit differentiation.

$5x^2+y^3=12$

Find $dy/dx$ for the equation below using implicit differentiation.

$xy=\(\sin\]\left\)(y\(\right\))$

66–71. Higher-order derivatives Find and simplify y''.

x + sin y = y

5–8. Calculate dy/dx using implicit differentiation.

x = y²

5–8. Calculate dy/dx using implicit differentiation.

sin y+2 = x

13-26 Implicit differentiation Carry out the following steps.

a. Use implicit differentiation to find dy/dx.

(x+y)^2/3=y; (4, 4)

Given that $3x-tany=4$, what is $\frac{dy}{dx}$ in terms of $y$?