Let z = g(x) = f--1(x) We need to find dz/dx x = f(z) Differentiating wrt x, 1 = f'(z) (dz/dx) where f'(z) represents the derivative of f(z) wrt z dz/dx = 1/f'(z)
Hence, dz/dx = 1/[6(2z - )2+2+sinz] Now, dz/dx| x = pi = |1/[6(2z - )2+2+sinz]|x=pi So we must find the value of z at at which x = f(z) is Now, by inspection we can see that the required value of z is /2 Hence, dz/dx| x = pi = |1/[6(2z - )2+2+sinz]|z=pi/2 = 1/3
Moderation Team
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)3+2x-cosx
)2+2+sinx
