I require to uncover \$fracddx(frac1sqrtx+2)\$ only using the basic an interpretation of the derivative \$f"(x)=lim_h o 0fracf(x+h)-f(x)h\$, but I"m not having any luck with the algebra. Any kind of hints?  By elementary school algebra (try it!) friend can present that\$\$fracf(x+h)-f(x)h=-frac1sqrtx+h+2,sqrtx+2,,(sqrtx+h+2+sqrtx+2)\$\$and that is then easy to discover the limit together \$h o0\$.

You are watching: Derivative of square root of x 1 \$\$fracddx frac1sqrtx+2=lim_h o0fracleft(frac1sqrtx+h+2-frac1sqrtx+2 ight)h\$\$

\$\$=lim_h o0fracleft(frac1sqrtx+h+2-frac1sqrtx+2 ight)h imesfracfrac1sqrtx+h+2+frac1sqrtx+2frac1sqrtx+h+2+frac1sqrtx+2\$\$

\$\$=lim_h o0fracleft(frac1x+h+2-frac1x+2 ight)hleft(frac1sqrtx+h+2+frac1sqrtx+2 ight)\$\$

\$\$=lim_h o0fracleft(frac-h(x+h+2)(x+2) ight)hleft(frac1sqrtx+h+2+frac1sqrtx+2 ight)\$\$

\$\$=lim_h o0fracleft(frac-1(x+h+2)(x+2) ight)left(frac1sqrtx+h+2+frac1sqrtx+2 ight)\$\$

\$\$=fracfrac-1(x+2)^2frac2sqrtx+2\$\$

\$\$=frac-12(x+2)^frac32\$\$

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answer Jun 2 "16 in ~ 4:48 Ian MillerIan müller
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