Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

Year 12s: what will be the first way you research your future options? >>

I have a few differentiation questions.

I don't know how to work these out, any help is appreciated.

1)

10^{x^2}

2)

\sin [ln(x^2)]

3)

V=Ee^{-t/RC}

diff. wrt to t

No. 3 lowercase e is for the e constant.

(edited 8 years ago)

Original post by cushticwarrior

I don't know how to work these out, any help is appreciated.

1)

10^{x^2}

2)

\sin [ln(x^2)]

3)

V=Ee^{-t/RC}

diff. wrt to t

No. 3 lowercase e is for the e constant.

All of these can be solved using the chain rule: for suitably differentiable functions

f

and

g

,

( f \circ g ) ^\prime (x) = g ^\prime (x) \times (f ^\prime \circ g ) (x)

For part (a), it may be helpful you use the fact that

a^b = e^{b \log a}

First one can be rewritten as: e^{(x^2)ln10}

^{Then use chain rule.}

^{The second one is just a function of a function of a function. Use chain rule twice.}

^{Third one is basic, just imagine the constants as numbers, should make it straightforward.}

(edited 8 years ago)

OP

thanks guys

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