Thread: 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.

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.

Thanks,

How did you differentiate e^2x?

The rule for differentiating exponentials is:

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

Use the chain rule: with y(x)= 2x, this is . Its derivative is

Originally Posted by HallsofIvy

Use the chain rule: with y(x)= 2x, this is . Its derivative is

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

I have managed to work it out now.

Thanks.