Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Sec. 5]_Derivatives of Higher Orders_69
687. Find the nth derivative of the function y = (
where n js 3 natural number.
688. Find the nth derivatives of the functions:
a ) y^T^x* and b ) y^^**'
689. Find the /zth derivative of the functions:
a) j/=sinx; e) y=^j\
b)4, = cos2*;
c) y = e~
f) = J/ yJ;
9
*; g) y=sin*jr,
d) |/=ln(l+x); h) y = l
690. Using the Leibniz rule, find y {n
\ if:
691. Find / (n)
(0), if
a) y = x.f\ d)y =
~
b) y = 2
jc .e-* x ; e) y = x*
2 = c) // (! A:
) cos x\
B. Higher-Order Derivatives of Functions Represented
Parametrically and of Implicit Functions
d^u
In the following problems find ^ .
692. a) K = \nt, b) x = arc tan/, c) * = arc sin/
' J x =
\0-l
693. _, ,
696. Find
:asin/;
"'
\ y = a(l -cos/);
: = 0cos'/, iv f x = a (sin/- /cos/),
f =
a(cos/-f-/ sin/).