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Differentiation watch

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    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 ???

    Thanks for your time.
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    (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
    howd you get that answer?
    I know your wrong because its the same answer then previous question and tan²x≠(2x)/cosx
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    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?
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    (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.
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    (Original post by dhokes)
    4) Given that x=cosy² Find dy/dx in terms of y

    Is this right, 2sec²xtanx ???

    Thanks for your time.
    d[x = cosy²]/dy
    dx/dy = -2ysiny²
    dy/dx = -1/2ysiny² = -cosecy²/2y

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