Question

I need help question

Answer 1

Given

`\begin{gathered} y=√(x)e^(x^3)(x^2+1)^6 \\ \\ \Rightarrow\ln(y)=\ln(√(x))+\ln(e^(x^3))+\ln((x^2+1)^6) \\ \\ \Rightarrow(1)/(y)(dy)/(dx)=(1)/(2x)+3x^2+6(2x)/((x^2+1)) \\ \\ \Rightarrow(dy)/(dx)=y((1)/(2x)+3x^2+(12x)/((x^2+1))) \end{gathered}`

=>

`y^(\prime)=√(x)e^(x^3)(x^2+1)^6((1)/(2x)+3x^2+(12x)/((x^2+1)))`