Final answer:
To differentiate y = arctan(3x), use the chain rule and the derivative of arctan(u) with respect to x. The derivative is 3/(1+9x^2).
Correct option is D
Step-by-step explanation:
To differentiate y = arctan(3x), we need to use the chain rule. The derivative of arctan(u) with respect to x is 1/(1+u^2) times the derivative of u with respect to x. In this case, u = 3x. So, applying the chain rule, the derivative of y = arctan(3x) becomes:
dy/dx = 1/(1+(3x)^2) * d(3x)/dx
dy/dx = 1/(1+9x^2) * 3
Simplifying further, we get:
dy/dx = 3/(1+9x^2)
Therefore, the correct answer is D. 3/(1+9x^2).