Find the Derivative - d/dx 2tan(3x)

Problem

(d(2)*tan(3*x))/d(x)

Solution

1. Identify the constant multiple rule, which allows the constant 2 to be moved outside the derivative.

(d(2)*tan(3*x))/d(x)=2d(tan(3*x))/d(x)

2. Apply the chain rule to the function tan(3*x) where the outer function is tan(u) and the inner function is u=3*x

d(tan(u))/d(u)=sec2(u)

3. Differentiate the inner function 3*x with respect to x

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

4. Multiply the derivative of the outer function by the derivative of the inner function and the constant.

2⋅sec2(3*x)⋅3

5. Simplify the expression by multiplying the coefficients.

6*sec2(3*x)

Final Answer

(d(2)*tan(3*x))/d(x)=6*sec2(3*x)

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