Question #1688

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

Expert's answer

y' = 1/(2√x) * e^{x^2} (x^{2}+3)^{5} + 2x√x e^{x^2} (x^{2}+3)^{5} +2x*5* √x e^{x^2} (x^{2}+3)^{4}

= e^{x^2}(x^{2}+3)^{4} (1/(2√x)(x^{2}+3) + 2x^{3}√x + 6x√x + 10x√x) = e^{x^2}(x^{2}+3)^{4}(1/2 * x√x +6x√x + 10x√x + 3/(2√x) + 2x^{3}√x) =

= e^{x^2}(x^{2}+3)^{4} (16.5x√x + 3/(2√x) + 2x^{3}√x)

= e

= e

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