Question

Find dy/dx , if Y= tan-1(5x/1-6x^2)

Answer 1

(5 - 90x²)/(sec²y(1 - 6x²)²]

tan y = 5x/(1 - 6x²)

Differentiate implicitly

sec²y dy/dx = [5(1 - 6x²) + 5x(-12x)]/(1 - 6x²)²

dy/dx = (5 - 90x²)/(sec²y(1 - 6x²)²]