Question

Derive a função f(x)=tan (x).e^3x

Paso a passo pf

Answer 1

f(x)=tan (x)  *  e^(3x)

f(x)=sen(x)/cos(x)  *  e^(3x)

f(x)'=[sen(x)/cos(x)]' *  e^(3x)  + (sen(x)/cos(x))  *  (e^(3x))'


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[sen(x)/cos(x)]'  =[(sen(x))' * cos(x)- sen(x) *(cos(x))'] /cos²(x)

[sen(x)/cos(x)]'  =[cos(x) * cos(x)- sen(x) *(-sen(x)] /cos²(x)

[sen(x)/cos(x)]'  =[cos²(x)+sen²(x)] /cos²(x)

[sen(x)/cos(x)]'  =[1] /cos²(x) =sec²(x)

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(e^(3x))' = (3x)' * e^(3x)  = 3*e^(3x)

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f(x)'=[sen(x)/cos(x)]' *  e^(3x)  + (sen(x)/cos(x))  *  (e^(3x))'

f(x)'=sec²(x)*  e^(3x)  + tan(x) * 3*e^(3x)

f(x)'=sec²(x)*  e^(3x)  + 3*tan(x)  * e^(3x)

f(x)'=e^(3x) * [sec²(x)   + 3*tan(x) ]