# Thread: Differentiating Trig functions

1. ## Differentiating Trig functions

Hi,

I am revising on "Differentiating Trig functions" and I am stuck on a question I am not so sure about. I understand the rules such as the quotient rule, product rule etc. But for this it's not working out.

Differentiate y = e^2x cos x

Thanks.

2. Hi, for this you need to use the product rule

y = uv, y' = uv' + u'v.

in this case u = e^2x and v = cosx

so u' = 2e^2x and v' = -sinx

combined this give y' = 2(e^2x)cosx - (e^2x)sinx

Hope that helps.

3. Thanks,

How did you differentiate e^2x?

4. The rule for differentiating exponentials is:

if y = e^ax, then y' = ae^ax.

5. Use the chain rule: with y(x)= 2x, this is $f(x)= e^{y}$. Its derivative is
$\frac{d e^{2x}}{dx}= \frac{d e^y}{dy}\frac{dy}{dx}$

6. Originally Posted by HallsofIvy
Use the chain rule: with y(x)= 2x, this is $f(x)= e^{y}$. Its derivative is
$\frac{d e^{2x}}{dx}= \frac{d e^y}{dy}\frac{dy}{dx}$
Hi HallsofIvy,

Could you please show me how to work it out following that method. I mean the full question: y = e^2x cos x

7. I have managed to work it out now.

Thanks.