Differentiation

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.

Reply 1

Malik

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=3e^3xx³+3e^3xx²
.......=3x²e^3x(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

Reply 2

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?

Reply 3

Malik

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.