(i) y = xe^-x^2 (ii) s(t) = 4√((t^3 + 1)/(t^3 - 1))

Question

Differentiate 

(i) y = xe^{-x^2}

(ii) \(s(t)=\sqrt[4]{\frac{t^3+1}{t^3-1}}\)

Answer 1

(i) y = xe^{-x^2} 

y = uv where u = x and v = e^{-x^2} 

Now u’ = 1 and v’ = e^{-x^2} (-2x)

v’ = – 2xe^{-x^2} 

Now y = uv ⇒ y’ = uv’ + vu’ 

(i.e.) dy/dx = x[-2xe^{-x^2}] + e^{-x^2} (1)

= e^{-x^2} (1 – 2x²)

(ii) s(t) = (t³ + 1)/(t³ - 1)^1/4

Let u = (t³ + 1/t³ - 1)

du/dt