Question 110417
{{{(d/dx)(sqrt(2-3x^2))}}} Start with the given function



{{{(d/dx)(1/2sqrt(2-3x^2))}}} Take the derivative of {{{sqrt(A)}}} (just the outside function) to get {{{1/2sqrt(A)}}}



{{{(d/dx)(1/2sqrt(2-3x^2))*(-6x)}}} Now take the derivative of the inside function {{{2-3x^2}}} to get {{{-6x}}}. Multiply {{{-6x}}} by {{{1/2sqrt(2-3x^2))}}}




{{{(-3x)/(sqrt(2-3x^2))}}} Reduce


So the derivative of {{{sqrt(2-3x^2)}}} with respect to x is 


{{{(-3x)/(sqrt(2-3x^2))}}}