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

Problem

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

Solution

1. Identify the outer, middle, and inner functions to apply the chain rule. The outer function is sin(u) the middle function is tan(v) and the inner function is 6*x

2. Apply the chain rule by differentiating the outer function sin(u) with respect to its argument, which gives cos(tan(6*x))

3. Differentiate the middle function tan(v) with respect to its argument, which gives sec2(6*x)

4. Differentiate the inner function 6*x with respect to x which gives 6

5. Multiply the results of the derivatives together according to the chain rule formula.

6. Simplify the expression by rearranging the constants and trigonometric terms.

Final Answer

d(sin(tan(6*x)))/d(x)=6*cos(tan(6*x))*sec2(6*x)

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