Question

Derivative of 5^(square root of w)

Answer 1

5sqrt(w)^sqrt(w)-1

Answer 2

\[\frac{ 1 }{ 2\sqrt{w} } * 5 ^{\sqrt{w}-1} *\ln|\sqrt{w}|\]

Answer 3

\(5^{\color{#ff1100}{\sqrt{w}}}\) follows the formula \(\large \color{#6633bb}{a} ^{\color{#ff1100}{x}} * \frac{ d }{ dx }(\color{#ff1100}{x})* \ln{\color{#6633bb}{a}}\)
By solving this according to the formula, we get \(\large \color{#6633bb}{5}^{\color{#ff1100}{\sqrt{w}}}*\frac{ 1 }{ \color{#ff1100}{2\sqrt{w}}}*\color{#6633bb}{\ln 5}\)

Answer 4

@mahdi2020 , you're taking the derivative and putting it into a^x formula...that doesnt work, remove the \(\sqrt{w}-1\)