Answer to Question #1688 in Calculus for Abhilash

Question

Use logarithmic differentiation to find the derivative of the function.
y = sqrt(x)e^x^2(x^2 + 3)^5

Answer 1

y' = 1/(2√x) * e^{x^2} (x²+3)⁵ + 2x√x e^{x^2} (x²+3)⁵ +2x*5* √x e^{x^2} (x²+3)⁴
= e^{x^2}(x²+3)⁴ (1/(2√x)(x²+3) + 2x³√x + 6x√x + 10x√x) = e^{x^2}(x²+3)⁴(1/2 * x√x +6x√x + 10x√x + 3/(2√x) + 2x³√x) =
= e^{x^2}(x²+3)⁴ (16.5x√x + 3/(2√x) + 2x³√x)