Find the Derivative - d/dx 6tan(x)

Problem

(d(6)*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 the function.

2. Apply the rule by moving the constant 6 outside of the derivative operator.

(d(6)*tan(x))/d(x)=6d(tan(x))/d(x)

3. Recall the standard derivative of the trigonometric function tan(x) which is sec^2(x)

d(tan(x))/d(x)=sec^2(x)

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

6⋅sec^2(x)=6*sec^2(x)

Final Answer

(d(6)*tan(x))/d(x)=6*sec^2(x)

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