Question

differentiate this -

Answer 1

\[y=\sqrt{x}e ^{x/2}(x ^{2}+1)^{10}\]

Answer 2

\[e^{\frac{x}{2}}(\frac{d}{dx}(\sqrt{x}(x^2+1)^{10})+\sqrt{x} (x^2+1)^{10}\frac{d}{dx}(e^{\frac{x}{2}}).......(1)\]first find d/dx(sqrt(x)(x^2+1)^(10)
\[\frac{d}{dx}(\sqrt{x}(x^2+1)^{10})=\frac{1}{2\sqrt{x}}(x^2+1)^{10}+10 \sqrt{x}(x^2+1)^{9} \times 2x\]\[=\frac{1}{2\sqrt{x}}(x^2+1)^{10}+20x \sqrt{x}(x^2+1)^{9}\]now d/dx(e^{x/2})\[\frac{d}{dx}(e^{\frac{x}{2}})=\frac{1}{2}e^{\frac{x}{2}}\]substitute in (1)
\[\frac{dy}{dx}=e^{\frac{x}{2}}[\frac{1}{2\sqrt{x}}(x^2+1)^{10}+20x \sqrt{x} (x^2+1)^9]+\sqrt{x}(x^2+1)^{10} \times \frac{1}{2}e^{\frac{x}{2}}\]

Answer 3

actually @lalaly - check out this video. http://www.youtube.com/watch?v=Q27MGfI1V70
but if i dont use logs, i get -
dy/dx = \[\sqrt{x}e ^{x ^{2}}.2x.10(x ^{2}+1)^{9}\]

Answer 4

i thought its e^(x/2)
but logarithmic differentiation is much simpler,,,

Answer 5

oops sorry it was x^2 not x/2 my bad..

Answer 6

yeah but the answers dont match