Let y =x arcsin x, x is an element of ]-1, 1[. Show that d^2y/dx^2 = 2-x^2/(1-x^2)^3/2
2 answers
I really need help on this!!!!
The secoind derivative of a product of two functions f(x) and g(x) is:
f''(x) g(x) + 2 f'(x) g'(x) + f(x)g''(x)
If you take f(x) = x and
g(x) = arcsin(x) then the first term is zero, so you only have to evaluate the last two terms. If you add them up you will get (2-x^2)/(1-x^2)^3/2.
f''(x) g(x) + 2 f'(x) g'(x) + f(x)g''(x)
If you take f(x) = x and
g(x) = arcsin(x) then the first term is zero, so you only have to evaluate the last two terms. If you add them up you will get (2-x^2)/(1-x^2)^3/2.
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