Question

Given that 3x – tan y = 4, what is dy/dx in terms of y?

Answer 1

Answer:

$\frac{dy}{dx}$ = 3 cos² y ⇒ B

Step-by-step explanation:

∵ 3x - tan(y) = 4

∵ The differentiation of tan(y) with respect to x is sec² y · dy/dx

∵ The differentiation of 3x with respect to x is 3

∵ the differentiation to 4 with respect to x is 0

∴ d/dx [3x - tan(y) = 4] is 3 - sec² y · dy/dx = 0

∵ 3 - sec²(y) · dy/dx = 0

→ Subtract 3 from both sides

∴ - sec² y · dy/dx = -3

→ Divide both sides by -1

∴ sec² y · dy/dx = 3

→ Divide both sides by sec²(x)

∴ $\frac{dy}{dx}=\frac{3}{sec^{2}y}$

→ Remember $\frac{1}{secy}$ = cos y

∵ $\frac{1}{sec^{2}y}$ = cos² y

∴  $\frac{3}{sec^{2}y}$ = 3 cos² y

∴ $\frac{dy}{dx}$ = 3 cos² y