Answer:
[tex]\frac{dy}{dx}[/tex] = 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)
∴ [tex]\frac{dy}{dx}=\frac{3}{sec^{2}y}[/tex]
→ Remember [tex]\frac{1}{secy}[/tex] = cos y
∵ [tex]\frac{1}{sec^{2}y}[/tex] = cos² y
∴ [tex]\frac{3}{sec^{2}y}[/tex] = 3 cos² y
∴ [tex]\frac{dy}{dx}[/tex] = 3 cos² y
