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Prep Problems for Engineers...blek

Just got started on this and it seems that some of the Maths I did during A Levels isn't present in my brain anymore... oh well... I didn't bring home any notes so I hope some of you can help me out...

1.1 Miscellaneous
2. (a) (ii) Differentiate with respect to x : sin^-1 (x^2) [arcsin X squared]

The answer is 2x/[sqrt(1 - x^4)]

There are like a hundred more questions to go... :frown:

:frown:

TQ!!!

SHH

Just got started on this and it seems that some of the Maths I did during A Levels isn't present in my brain anymore... oh well... I didn't bring home any notes so I hope some of you can help me out...

1.1 Miscellaneous
2. (a) (ii) Differentiate with respect to x : sin^-1 (x^2) [arcsin X squared]

The answer is 2x/[sqrt(1 - x^4)]

There are like a hundred more questions to go... :frown:

:frown:

TQ!!!

From first principles:
Let x=siny
Then: dx=cosy dy => 1/cosy=dy/dx => 1/sqrt(1-x^2)=d(arcsinx)/dx.
So, when you differentiate arcsin(x^2), you get 1/sqrt(1-x^4); however, because it's a function of a fuction, you also have to differentiate the x^2, and that's where the 2x comes from. Hence 2x/sqrt(1-x^4)

OP

Thanks!

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