Differentiate: tan(2x) cos(x)
- Explain the product rule: d/dx ( f(x) . g(x) ) = f'(x).g(x) = g'(x) . f (x)
2. Briefly run through trigonometric derivatives.* cos (x) differentiates to: -sin(x)* tan (x) differentiates to: sec^2 (x)
3. Briefly run through the chain rule.* tan (2x) differentiates to: 2 sec^2 (2x)
4. Bring everything together to get the two terms for the answer
* First term of the solution is: [ 2 sec^2 (2x) . cos (x) ]* Second term of the solution is: [ - sin (x) . tan (2x) ]
* Final Solution is: [ 2 sec^2 (2x) . cos (x) ] + [ - sin (x) . tan (2x) ]
