Find the Derivative - d/dx y=2tan(x)

Problem

d()/d(x)*2*tan(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 constant multiple rule by pulling the constant 2 outside of the derivative operator.

(d(2)*tan(x))/d(x)=2d(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 by the resulting derivative to find the final expression.

2⋅sec2(x)=2*sec2(x)

Final Answer

(d(2)*tan(x))/d(x)=2*sec2(x)

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