Find the derivative of `f(x)=3x^2+e^(-2x)` :

The derivative of a sum is the sum of the derivatives;

The derivative of `3x^2` is `6x` using the power and constant rules.

The derivative of `1/(e^(2x))=e^(-2x)` is `-2e^(-2x)` (`d/(dx)e^u=e^u(du)/(dx)` where u is a differentiable function of x)

Thus if `f(x)=3x^2+e^(-2x)` then:

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`f'(x)=6x-2e^(-2x)` or `6x-1/(e^(2x))`

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The derivative of *f(x)=3x2+e-2x *

* 3x2 derivative is from the formula of derivative is xn= n*xn-1 so, 3x2=2*3x2-1=6x *

*The derivative of e-2x is from the formula of ef(x) is = ef(x) *f’(x) *

*e-2x = e-2x *(-2x)’ derivative which is equal to = e-2x *(-2) *

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*F’(x)=3x2+e-2x=6x+ e-2x *(-2) or 6x+ (-2)|e2x*

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* *