Understanding Chain Rule: Derivatives and the Quotient Rule Explained

[juice34]

Could someone explain this to me please where n=y/squareroot(4vt)

∂C/∂t=(dC/dn)(∂n/∂t)=-(1/2)(n/t)(dC/dn)

When i take the derivative of 1/t^1/2 i get -(1/2)t^(-3/2) so where does the (-3/2) go to in the final answer of -(1/2)(n/t)(dC/dn). Thank you very much!

 

[LCKurtz]

$$n = \frac y 2 v^{-\frac 1 2}t^{-\frac 1 2}$$

$$n_t = \frac y 2 v^{-\frac 1 2}(-\frac 1 2)t^{-\frac 3 2} = \frac y 2 v^{-\frac 1 2}t^{-\frac 1 2}(-\frac 1 2)t^{-1} = (-\frac 1 2)\frac n t$$

 

[juice34]

Thank you soooooo much!