Differentiate: tan(2x) cos(x)

  1. 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) ]
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