Obtain the derivative of  `h(x) = (1-e^(2x))^3`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The derivative of `h(x) = (1-e^(2x))^3` has to be determined. Using the chain rule:

`h'(x) = 3*(1 - e^(2x))^2*(-e^(2x))*2`

=> `-6*(1 - e^(2x))^2*e^(2x)`

The derivative of `h(x) = (1-e^(2x))^3` is `h'(x) = -6*(1 - e^(2x))^2*e^(2x)`

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted on

h(x) =(1-e^2x)^3

Direvative of h(x) means h'(x)

h'(x) = d((1-e^2x)^3)/dx

 

If h(x)=[f(x)]^n;

h'(x) = {n[f(x)]^(n-1)}*f'(x) where f'(x) is derivative of f(x)

 

Also d(e^(nx))/dx = n*e^(nx)

 

In the question f(x) = (1-e^2x)

Then f'(x) = (-2*e^2x)

 

so h'(x) = {n[f(x)]^(n-1)}*f'(x)

            = {3*[(1-e^2x)]^(3-1)}*(-2*e^2x)

 

   h'(x) = [-6*e^2x][(1-e^2x)^2]

 

 

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