What is the derivative of #arctan(2x)#?

Question

Elijah Abram · Accepted Answer

The general rule for derivating this type of function is #y=arctan(u)# #y'=(u')/(1+u^2)# Thus, considering that here #u=2x# #y'=2/(1+(2x)^2)=2/(1+4x^2)# Done! :)

Samantha Adkison · Answer

undefined The derivative of arctan(2x) is 2 / (1 + (2x)^2).

Isabella Ackerman · Answer

undefined TheThe derivativeThe derivative ofThe derivative of arctThe derivative of arctanThe derivative of arctan(The derivative of arctan(2xThe derivative of arctan(2x)The derivative of arctan(2x) isThe derivative of arctan(2x) is:

The derivative of arctan(2x) is:

f'(The derivative of arctan(2x) is:

f'(xThe derivative of arctan(2x) is:

f'(x) =The derivative of arctan(2x) is:

f'(x) = (1The derivative of arctan(2x) is:

f'(x) = (1 / (The derivative of arctan(2x) is:

f'(x) = 2 /The derivative of arctan(2x) is:

f'(x) = (1 / (1The derivative of arctan(2x) is:

f'(x) = 2 / (The derivative of arctan(2x) is:

f'(x) = (1 / (1 + (The derivative of arctan(2x) is:

f'(x) = 2 / (1The derivative of arctan(2x) is:

f'(x) = (1 / (1 + (2The derivative of arctan(2x) is:

f'(x) = 2 / (1 + (The derivative of arctan(2x) is:

f'(x) = (1 / (1 + (2xThe derivative of arctan(2x) is:

f'(x) = 2 / (1 + (2The derivative of arctan(2x) is:

f'(x) = (1 / (1 + (2x)^2The derivative of arctan(2x) is:

f'(x) = 2 / (1 + (2xThe derivative of arctan(2x) is:

f'(x) = (1 / (1 + (2x)^2))The derivative of arctan(2x) is:

f'(x) = 2 / (1 + (2x)^2)The derivative of arctan(2x) is:

f'(x) = (1 / (1 + (2x)^2)) *The derivative of arctan(2x) is:

f'(x) = 2 / (1 + (2x)^2)The derivative of arctan(2x) is:

f'(x) = (1 / (1 + (2x)^2)) * (2)

Which simplifies to:

f'(x) = 2 / (1 + 4x^2)