Find the derivative of y=(2−x^2)^x. Be sure to include parentheses around the arguments of any logarithmic functions in your answer.

Answer 1

ln y = x ln(2-x²)

(1/y)(dy/dx) = [-2x²/(2-x²)] + ln(2-x²)

Now use the original expression for y to write dy/dx as a function of x alone...be careful, the expression is MESSY!