Find the Derivative - d/dx 5arctan(x)

Problem

d()/d(x)*5*arctan(x)

Solution

1. Identify the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.

d()/d(x)*5*arctan(x)=5d(arctan(x))/d(x)

2. Apply the formula for the derivative of the inverse tangent function, which is d(arctan(x))/d(x)=1/(1+x2)

5d(arctan(x))/d(x)=5⋅1/(1+x2)

3. Simplify the expression by multiplying the constant into the numerator.

5⋅1/(1+x2)=5/(1+x2)

Final Answer

d()/d(x)*5*arctan(x)=5/(1+x2)

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