Differentiate a negative

joeperry

Hi, Substitute u for the inner function, use the chain rule to calculate dy/dx
y = e^-x^2

i'm not sure what happens when i differentiate a negative.

Does -x^2 become -2x?

Answer i got was, e^-x^2.-2x

Am i right? Thanks.

TheBody

Hi op. Yea, your answer is spot on.

The basic rule of differentiation is [latex]\frac{d}{dx}x^n=nx^{n-1}[/latex].

joeperry

Hi great thanks

What about this one, it's the same kind as above. Do i drop the 6 when i differentiate?

y = 6tan(3x+1)

I got, sec^2(3x+1).3

Is this right please?

TheBody

No, you need to keep the 6. I guess to elaborate on the rule I have above,
[latex]\frac{d}{dx}cx^n=c\frac{d}{dx}x^n=cnx^{n-1}[/latex] where c is just a constant. In other words, you can take a constant out of the differentiation operation and multiply the result by the constant when you have finished the differentiation.

joeperry

Thanks a lot . Now i get, 18sec^2(3x+1)

Is that correct?

TheBody

Yea, that correct. Well done!!

joeperry

Hi have another one for somebody

y = ln(3-4cosx)

What do i substitute u = for?

Is it everything in the bracket or do i only use 4cosx = u? cosx =u? Thanks

TheBody

Let [latex]u=3-4 \cos x [/latex] is the way to go!

joeperry

Hey buddy thanks, so i ended up with 4sinx.1/3-4cosx

i think thats correct?

TheBody

While practising the chain rule is a worthwhile thing to do, the derivatives of trig, log and exponential functions come up so often, it can be useful to just learn off a few shortcut formulae. Here are ones you might consider:

[latex]\frac{d}{dx}\cos f(x)= -f'(x) \sin f(x)[/latex]
[latex]\frac{d}{dx}\sin f(x)= f'(x) \cos f(x)[/latex]
[latex]\frac{d}{dx}\ln f(x)= \frac{f'(x)}{f(x)}[/latex]
[latex]\frac{d}{dx}e^{f(x)}= f'(x)e^{f(x)}[/latex]

So for example, [latex]\frac{d}{dx}\cos (6x^2+x)=-(12x+1) \sin (6x^2+x)[/latex]

All the above rules are easy to find using the chain rule.

TheBody

joeperry wrote: »

Hey buddy thanks, so i ended up with 4sinx.1/3-4cosx

i think thats correct?

Looks good to me.

joeperry

I can see from that now,that in my last question i should have ended up with 4sinx/3-4cosx

Thanks!