How do you find the derivative of #arcsin(x^2/4)#?
1 Answer
# d/dx arcsin(x^2/4) = x/(2sqrt(1-x^4/16)) #
Explanation:
We use the following derivatives:
# {: (ul("Function"), qquad ul("Derivative"), qquad ul("Notes")), (f(x), qquad f'(x),), (af(x), qquad af'(x),qquad a " constant"), (x^n, qquad nx^(n-1), qquad n " constant (Power rule)"), (sin^(-1)x, qquad 1/sqrt(1-x^2), ), (f(g(x)), qquad f'(g(x)) \ g'(x),qquad "(Chain rule)" ) :} #
So that:
# d/dx arcsin(x^2/4) = 1/sqrt(1-(x^2/4)^2) d/dx (x^2/4) #
# " " = 1/sqrt(1-x^4/16) * (2x)/4 #
# " " = 1/sqrt(1-x^4/16) * x/2 #
# " " = x/(2sqrt(1-x^4/16)) #
