find the value of dy/dx when x=1 (a are constant)
i)y=(√x-3)(√x-4) *only the x are under the square root
ii)y=a/x - x/a
iii)y=3(4x^-1 - 2x^-2)
+118723 find the value of dy/dx when x=1 (a are constant)
i)y=(√x-3)(√x-4) *only the x are under the square root
\(y=(\sqrt{x}-3)(\sqrt{x}-4)\\ \qquad let\\ \qquad u=x^{0.5}-3 \qquad v=x^{0.5}-4\\ \qquad u'=0.5x^{-0.5} \qquad v=0.5x^{-0.5}\\ y'=uv'+vu' \\ \mbox{Can you finish it?}\)
ii)y=a/x - x/a
\(y=ax^{-1}-\frac{x}{a}\\ y'=-1ax^{-2}-\frac{1}{a}\\ y'(1)=-1-\frac{1}{a}\)
iii)y=3(4x^-1 - 2x^-2)
\(y=3(4x^{-1}-2x^{-2})\\ y'=3(-4x^{-2}+4x^{-3})\\ y'(1)=3(-4+4)=0\)
