A problem on second order differentiation

Question

If $y=\sin x$, then find the value of $$\frac{d^2(\cos^7 x)}{dy^2}$$

I have no idea on how to proceed in this problem. Please help.

You can use the chain rule $\frac{dy}{dz} = \frac{dy}{dx}\cdot\frac{dx}{dz}$. Then do another differentiation to derive a chain rule in the 2nd order. — meta_warrior, Nov 02 '13 at 14:19

score 3 · Accepted Answer · answered Nov 02 '13 at 14:24

3

Hint: notice that

$$ \cos x = \sqrt{1-y^2}$$

answered Nov 02 '13 at 14:24

Mhenni Benghorbal

score 0 · Answer 2 · answered Nov 02 '13 at 14:23

0

You can also start replacing x by ArcSin[y] and remember that Cos[ArcSin[z]]=Sqrt[1-z^2]. Can you continue with this ?

answered Nov 02 '13 at 14:23

Claude Leibovici

2 Answers2