4. Applications of Derivatives

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

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)

Use implicit differentiation to find dy/dx.

sin xy = x+y

Use implicit differentiation to find dy/dx.

e^xy = 2y

Use implicit differentiation to find dy/dx.

cos y² + x = e^y

Use implicit differentiation to find dy/dx.

x³ = (x + y) / (x - y)

27–40. Implicit differentiation Use implicit differentiation to find dy/dx.

6x³+7y³ = 13xy

27–40. Implicit differentiation Use implicit differentiation to find dy/dx.

√x⁴+y² = 5x+2y³

Surface area of a cone The lateral surface area of a cone of radius r and height h (the surface area excluding the base) is A = πr√r²+h².

b. Evaluate this derivative when r=30 and h=40.