IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

ekbana_bombabu

1. Let f(x) be a polynomial. then what is the second order derivative of f(e^x) .

2. if x = f(t) and y = g(t), then d^2/dx^2 is equal to

(a) f'g"-g'f"/(f')^3 (b) f'g"-g'f"/(f')^2

(c) g"/f" (d) f'g'-g"f'/(g')^3

.

him26.89

1) e^x{f '(e^x)}

2) c option.

first find dx/dt &dy/dt &so on

&then divide both.

nunoxic

2. if x = f(t) and y = g(t), then d^2/dx^2 is equal to

dx/dt = f'(t)..............................(1)
dy/dt = g'(t).............................(2)
dy/dx = g'(t)/f'(t)

d2y/dx2 = f'(t) g"(t) - g'(t) f " (t) / [f"(t)]^2 entire into dt/dx
=f'(t) g"(t) - g'(t) f " (t) / [f"(t)]^2 f'(t) (from 1)

nunoxic

2. if x = f(t) and y = g(t), then d^2/dx^2 is equal to

dx/dt = f'(t)..............................(1)
dy/dt = g'(t).............................(2)
dy/dx = g'(t)/f'(t)

d2y/dx2 = f'(t) g"(t) - g'(t) f " (t) / [f"(t)]^2 entire into dt/dx
=f'(t) g"(t) - g'(t) f " (t) / [f'(t)]^2 f'(t) (from 1)
= f'(t) g"(t) - g'(t) f " (t) / [f'(t)]^3
= A

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