Differentiating questions. (1 Viewer)

[basketcase89]

I was doing a past paper when I came across these questions that I'm quite sure I've done incorrectly:

(1) (2e^x - 4lnx)^9

I got: 9.(2e^x - 4/x).(2e^x - 4lnx)^8

(2) ln(cos5x)^6

(3) x^2 sinx + [sin^2(x/2) + cos^2(x/2)/3]

If anyone can shed some light on these I'd be forever grateful.

Thanks.

P.S. Does anyone think these are borderline 3 unit questions?!

 

[watatank]

I was doing a past paper when I came across these questions that I'm quite sure I've done incorrectly:

(1) (2e^x - 4lnx)^9

I got: 9.(2e^x - 4/x).(2e^x - 4lnx)^8

(2) ln(cos5x)^6

(3) x^2 sinx + [sin^2(x/2) + cos^2(x/2)/3]

If anyone can shed some light on these I'd be forever grateful.

Thanks.

P.S. Does anyone think these are borderline 3 unit questions?!

i) the first ones right.

ii) what is raised to the power 6? the whole thing on the cos5x?

 

[jemsta]

ii) just use log rules
ln(cos 5x)^6
= 6ln(cos5x)
= 6.(-5sin5x/cos5x)

is that the correct answer?

 

[watatank]

(3) x^2 sinx + [sin^2(x/2) + cos^2(x/2)/3]

If anyone can shed some light on these I'd be forever grateful.

Thanks.

P.S. Does anyone think these are borderline 3 unit questions?!

with question 3, what is being divided by 3 exactly? because if its [ sin^2(x/2) + cos^2(x/2) ] / 3 then you could just use the fact that sin^2(x/2) + cos^2(x/2) = 1 then its simply the product rule with the first thingo.

(d/dx) x^2 sinx + [sin^2(x/2) + cos^2(x/2)/3]

= (d/dx) x^2 sinx + [1/3]

= 2xsinx + x^2cosx

what year is it? none of those questions seem exceptionally hard, the methods are the same, just the algebra manipulation may be a little tougher.