Question

plz plz plz send fast​

Answer 1

Answer:

Step-by-step explanation:

Let y = tan^-1[5x/(1 - 6x^2)]

Then

tany = 5x/(1 - 6x^2)

Differentiating both sides

sec^2(y)dy/dx = [5(1 - 6x^2) - (5x)(- 12x)]/[1 - 6x^2]^2

= [5 - 30x^2 + 60x^2]/[1 - 6x^2]^2]

= [ 5 + 30x^2]/[1 - 6x^2]^2]

dy/dx = [ 5 + 30x^2]/[1 - 6x^2]^2] * [ 1/sec^2(y)]

= [ 5 + 30x^2]/[1 - 6x^2]^2] * cos^2[tan^-1(5x/(1 - 6x^2)]