Find the Derivative - d/dx arctan(2x)

Problem

d(arctan(2*x))/d(x)

Solution

1. Identify the outer function and the inner function to apply the Chain Rule. The outer function is arctan(u) and the inner function is u=2*x

2. Recall the derivative formula for the inverse tangent function, which is d(arctan(u))/d(u)=1/(1+u2)

3. Apply the Chain Rule by multiplying the derivative of the outer function by the derivative of the inner function.

d(arctan(2*x))/d(x)=1/(1+(2*x)2)⋅(d(2)*x)/d(x)

4. Differentiate the inner function 2*x with respect to x which results in 2

d(arctan(2*x))/d(x)=1/(1+4*x2)⋅2

5. Simplify the expression by multiplying the constants.

d(arctan(2*x))/d(x)=2/(1+4*x2)

Final Answer

d(arctan(2*x))/d(x)=2/(1+4*x2)

Want more problems? Check here!