Can anybody please help me out, i can't figure out how to work this one
Asked
Active
Viewed 90 times
1
-
See How to find a partial derivative of an implicitly defined function at a point; many other examples are found by searching for implicit partial derivative – Mar 08 '15 at 05:39
1 Answers
2
$$3y=z^3+3xz$$ $$0=3z^2\frac{\delta z}{\delta x}+3z+3x\frac{\delta z}{\delta x}$$ $$0=z^2\frac{\delta z}{\delta x}+z+x\frac{\delta z}{\delta x}$$ $$z=-(z^2+x)\frac{\delta z}{\delta x}$$
from $$0=z^2\frac{\delta z}{\delta x}+z+x\frac{\delta z}{\delta x}$$ $$0=2z(\frac{\delta z}{\delta x})^2+z^2\frac{\delta^2 z}{\delta x^2}+\frac{\delta z}{\delta x}+\frac{\delta z}{\delta x}+x\frac{\delta^2 z}{\delta x^2}$$ $$\frac{\delta^2 z}{\delta x^2}(z^2+x)=-2(z(\frac{\delta z}{\delta x})^2+\frac{\delta z}{\delta x})$$ taking in account that $$\frac{\delta z}{\delta x}=\frac{-z}{z^2+x}$$ follow that $$\frac{\delta^2 z}{\delta x^2}=\frac{2xz}{(z^2+x)^3}$$
Adi Dani
- 16,949
-
Thanks alot adi...if possible can you please elaborate a little, i am confused about the last part. 0=z2δzδx+z+xδzδx 0=2z(δzδx)2+z2δ2zδx2+z+δzδx+xδ2zδx2 – Ali Baloch Mar 08 '15 at 06:19
-
@AliBaloch Take the derivatives of both sides with respect to $x$. (Product rule + implicit differentiation) – White Shirt Mar 08 '15 at 06:59
-
@Adi Dani if possible could you please explain how to get to the final answer from third last & second last line :p – Ali Baloch Mar 08 '15 at 16:21