172 EXAMPLES OF DIFFERENTIAL COEFFICIENTS. 



3 KvF-aaT ^ = _^2/_ 



11 ye dx x(l+ny}' 



4. if **-/=(), 



. 



dx x xy log x 

 5. If ( a + 2,) 2 (&'-/)4-(*+)Y = 0, find . 



6. If sin (a?y) = wa;, find -^ . 



Hw 



7. Given y + a; s -3aay = 0, shew that ^ = -- 1^_. 



<c a (/ - au:) 3 



8. Given x* + 2ax*y = ay*, find -^ and ^4 an d write down 



the third derived equation. 



9. If y = ^ (x, y } u) and -^ (a;, y, w) = 0, find -- . 



d^r d<f) dty d<j> dty 



7? n du _ dx dy dy dx dx 



dx (ty d<f) d^f d^ d-^r ' 



du dy dy du du 



JO. If u = <p (x, y}, and w = % (#), find -y- . 



ay 



11. If M = a** + \/(sec;e;z/), find -y- , (1) when a; and ^ are 



independent, (2) when x + y = a. 

 12. If a? + VCsec xy} = 0, find ^ . 



Result -^ = - 



tan ^- y + 



^ic 1 ' log a log a; 



