Question 991362
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(a). {{{ y=tan^3(e^(5x)) }}}


Many times apply the chain rule for a derivative:


{{{dy/dx}}} = . . . . . . . . . . . . . . . . . . . (use the formula   {{{(d/dx)(x^3)}}} = {{{3x^2}}}  first;   it gives)


= {{{3tan^2(e^(5x))*(d/dx) (tan(e^(5x))) }}} = . . . . (then use the formula {{{(d/dx)(tan(x))}}} = {{{1/cos^2(x)}}};   it gives)


=  {{{3tan^2(e^(5x))}}}*{{{1/cos^2(e^(5x)))}}}*{{{(d/dx) (e^(5x))}}} = 


=  {{{3tan^2(e^(5x))}}}*{{{1/cos^2(e^(5x)))}}}*{{{5*e^(5x)}}}.