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# Differentiation watch

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1. From a Mock C3 Paper.

Differentiate with respect to x:

1) x^3 e^(3x)

Is this right, 3x²e^(3x) (x+1) ???

2) 2x/(cosx)

Is this right, 2secx(1+xtanx) ???

3) tan²x

Is this right, 2secx(1+xtanx) ???

4) Given that x=cosy² Find dy/dx in terms of y

Is this right, 2sec²xtanx ???

2. (Original post by dhokes)
From a Mock C3 Paper.

Differentiate with respect to x:

1) x^3 e^(3x)

Is this right, 3x²e^(3x) (x+1) ???
1)
dy/dx=3e3xx³+3e3x
.......=3x²e3x(x+1)
correct

2) 2x/(cosx)

Is this right, 2secx(1+xtanx) ???
2) dy/dx= (2cosx+2xsinx)/cos²x
.......=2cosx/cos²x +2xsinx/cos²x
.......=2secx(1+(xsinx/cosx))
.......=2secx(1+xtanx)
correct

3) tan²x

Is this right, 2secx(1+xtanx) ???
dy/dx=2tanxsec²x
I know your wrong because its the same answer then previous question and tan²x≠(2x)/cosx
3. Sorry that is what i meant, i wrote down the wrong thing, thanks for checking them and I dont suppose you know how to do the last one?
4. (Original post by dhokes)
Sorry that is what i meant, i wrote down the wrong thing, thanks for checking them and I dont suppose you know how to do the last one?
4) Given that x=cosy² Find dy/dx in terms of y

To be honest I am not familar with this type of question ive delt with cos²y but not cosy² I could hazard a guess at it but wouldnt want to look stupid.
5. (Original post by dhokes)
4) Given that x=cosy² Find dy/dx in terms of y

Is this right, 2sec²xtanx ???

d[x = cosy²]/dy
dx/dy = -2ysiny²
dy/dx = -1/2ysiny² = -cosecy²/2y

I think ..
6. (Original post by Dekota)
d[x = cosy²]/dy
dx/dy = -2ysiny²
dy/dx = -1/2ysiny² = -cosecy²/2y

I think ..
Yeah I agree with this but more importantly so does calc101 .
7. (Original post by Malik)
Yeah I agree with this but more importantly so does calc101 .
does anyone disagree with this?

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Updated: November 14, 2005
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