Question

y = ktan^-1(kx) find dy/dx​

Answer 1

Answer:

k²/(1 + k²x²)

Step-by-step explanation:

⇒ y = ktan⁻¹ (kx)

Differentiate with respect to x:

⇒ dy/dx = d(k tan⁻¹ (kx))/dx

⇒ y' = k d( tan⁻¹(kx) )/dx

 Using chain rule,

⇒ y' = k d( tan⁻¹(kx) )/d(kx)  × d(kx)/dx

⇒ y' = k [ 1/(1 + (kx)² ] × (k × 1)

⇒ y' = k²/(1 + k²x²)