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

Problem

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

Solution

1. Identify the outer, middle, and inner functions to apply the chain rule, where the expression is of the form ƒ*(g*(h(x)))

2. Differentiate the outer function sin(u) with respect to its argument u=tan(2*x) which gives cos(tan(2*x))

3. Differentiate the middle function tan(v) with respect to its argument v=2*x which gives sec2(2*x)

4. Differentiate the inner function 2*x with respect to x which gives 2

5. Multiply the results from the previous steps together according to the chain rule.

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

Final Answer

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

Want more problems? Check here!