Q.87. Derivatives.

Question  87.
Find da/db and d^2 a/db^2 given the following equation.
a^2+b+sin(a) = 2
 
Answer 87.
a^2+b+sin(a) = 2
Differentiating w.r.t. b,
2a*da/db + 1 + cosa*da/db = 0
(2a + cosa) da/db = -1
=> da/db = -1/(2a + cosa)

 d^2 a /db^2
= d/db(da/db)
= d/da(da/db) * da/db
= d/da[-1/(2a + cosa) * [-1/(2a + cosa)]
= (2 - sina)/(2a + cosa)^2 *[-1/(2a + cosa)]
= - (2 - sina) / (2a + cosa)^3
= (sina - 2) / (2a + cosa)^3

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