find derivative f(x)= 3x^2+1/e^2x

Expert Answers
embizze eNotes educator| Certified Educator

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:


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



ume2 | Student

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)


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