1. Derivative

Given:

Q(x) =4x^2 + 20x + 25/ e^x

Find Stationary Point and give its functional value.

Now, I know how to go about getting the answer (ie. get the first and second derivative). Question is, what is the derivate of Euler's number to the x power?

2. Differentiating

Hello ibrox
Originally Posted by ibrox
Given:
Originally Posted by ibrox
Q(x) =4x^2 + 20x + 25/ e^x

Find Stationary Point and give its functional value.

Now, I know how to go about getting the answer (ie. get the first and second derivative). Question is, what is the derivate of Euler's number to the x power?

$\displaystyle \frac{d}{dx}(e^x) = e^x$

But you'll need to write $\displaystyle \frac{25}{e^x}$ as $\displaystyle 25e^{-x}$, whose derivative is $\displaystyle -25 e^{-x}$. But you'll still have some difficulty in finding where $\displaystyle \frac{dQ}{dx}=0$. It's not a straightforward equation to solve...

3. Originally Posted by ibrox
Given:

Q(x) =4x^2 + 20x + 25/ e^x

Find Stationary Point and give its functional value.

Now, I know how to go about getting the answer (ie. get the first and second derivative). Question is, what is the derivate of Euler's number to the x power?
1. If $\displaystyle f(x)=e^x$ then $\displaystyle f'(x)=e^x$

2. Probably you mean:

Q(x) =(4x^2 + 20x + 25) / e^x

If so use the quotient rule:

$\displaystyle Q'(x)=\dfrac{e^x(8x+20) - (4x^2+20x+25)\cdot e^x}{e^{2x}}$

3. Factor out the $\displaystyle e^x$ in the numerator and cancel. Afterwards collect like terms in the numerator. You'll get:

$\displaystyle Q'(x)=\dfrac{-4x^2-12x-5}{e^x}$

4. I'll leave all further examinations for you.