Question

if x=2^√x then find the derivative of y with respect to x​

Answer 1

Answer:

y= 2^√y

Step-by-step explanation:

thats your answer

Answer 2

Answer:

$\color{blue} \bold{ \boxed{\frac{dy}{dx} = \frac{{2}^{ \sqrt{x} - 1 } }{2}log2}}$

Step-by-step explanation:

$\bold{y = {2}^{ \sqrt{x} } } \\ \\ = > apply \: log \\ \\ \bold{log \: y = log \: {2}^{ \sqrt{x} } } \\ \\ = > log {x}^{y} = y \: logx \\ \\ \bold{log \: y = \: \sqrt{x} \: log \: 2} \\ \\ = > diff \: \: wrt \: \: \: x \\ \\ \frac{d}{dx} (logx) = \frac{1}{x} \\ \\ \frac{d}{dx} {x}^{n} = n {x}^{n - 1} \\ \\ \bold{ \frac{1}{y} \frac{dy}{dx} = \frac{1}{2 \sqrt{x} } log2} \\ \\ \bold{ \frac{dy}{dx} = \frac{y}{2 \sqrt{x} } log2} \\ \\ \bold{ \frac{dy}{dx} = \frac{{2}^{ \sqrt{x} - 1 } }{2}log2}$

$<blue><bold><marquee> HOPE IT HELPS$