Find the Derivative - d/dx 3tan(x)

Problem

(d(3)*tan(x))/d(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 that function.

2. Apply the constant multiple rule by moving the coefficient 3 outside of the derivative operator.

(d(3)*tan(x))/d(x)=3d(tan(x))/d(x)

3. Recall the standard trigonometric derivative for the tangent function, which is sec2(x)

d(tan(x))/d(x)=sec2(x)

4. Multiply the constant 3 by the result of the derivative to find the final expression.

3⋅sec2(x)=3*sec2(x)

Final Answer

(d(3)*tan(x))/d(x)=3*sec2(x)

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