1. ## [SOLVED] Derivative notation confusion

Hi,

I'm confused as to what this notation means in this question.

The question is: Find each of the following:

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

so does that mean that the original function $\displaystyle e^x f(x)$ and then I find a general rule for it's derivative in respect to x?

Just, I'm used to things that are like: $\displaystyle \frac{d}{dx}(5x^2+5)$ so having something with the $\displaystyle \frac{d(blah)}{dx}$ is new and I'm not to sure what i means

Thanks!

2. Originally Posted by rudders93
Hi,

I'm confused as to what this notation means in this question.

The question is: Find each of the following:

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

so does that mean that the original function $\displaystyle e^x f(x)$ and then I find a general rule for it's derivative in respect to x?

Just, I'm used to things that are like: $\displaystyle \frac{d}{dx}(5x^2+5)$ so having something with the $\displaystyle \frac{d(blah)}{dx}$ is new and I'm not to sure what i means

Thanks!
Dear rudders93,

It's a multiplication of two functions, therefore you could used the product rule,

$\displaystyle \frac{d}{dx}[e^xf(x)]=e^x\frac{d}{dx}f(x)+e^xf(x)$

3. Originally Posted by rudders93
Hi,

I'm confused as to what this notation means in this question.

The question is: Find each of the following:

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

so does that mean that the original function $\displaystyle e^x f(x)$ and then I find a general rule for it's derivative in respect to x?

Just, I'm used to things that are like: $\displaystyle \frac{d}{dx}(5x^2+5)$ so having something with the $\displaystyle \frac{d(blah)}{dx}$ is new and I'm not to sure what i means

Thanks!
I’m pretty sure d/dx.(e^x.f(x)) means the same as d.(e^x.f(x))/dx otherwise the question doesn’t make sense.
Means the derivative of the e^x.f(x)

4. Ah awesome. Thanks!