I"m trying to number out if the \$fracddx sqrtf(x) = fracf"(x)2sqrtf(x)\$If possible can you provide me the proof for the function? First we convert the square source to exponent notation.

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\$fracddx sqrtf(x)= fracddx f(x)^frac12 \$

Then take the derivative and also apply the chain rule. That exponent is \$-frac12\$, because that some reason the markup language is do it hard to see the an unfavorable sign.

\$= frac12 f(x)^frac-12f"(x)\$

Converting back to notation v a square root symbol...

\$= frac12frac1sqrtf(x) f"(x)\$

And multiply.

\$= fracf"(x)2sqrtf(x)\$ Another possible way is logarithmic differentiation \$\$g(x)=sqrtf(x)\$\$ \$\$logig(g(x)ig)=frac 12 logig(f(x)ig)\$\$ \$\$fracg"(x)g(x)=frac 12fracf"(x)f(x)\$\$ \$\$g"(x)=frac 12fracf"(x)f(x)g(x)=frac 12fracf"(x)f(x)sqrtf(x)=frac 12fracf"(x)sqrtf(x)\$\$ Thanks for contributing solution to chrischona2015.org Stack Exchange!

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