What is the derivative of $y=2^(s^2)$ ?

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Answer 1 · 2015-08-09T15:48:40

$2(2^(s^2))sln2$

Perform logarithmic differentiation

Take natural logarithm of both sides

$lny=ln2^(s^2)$

Rewrite right hand side using properties of logarithms

$lny=s^2ln2$

Differentiate both sides with respect to $s$

$1/y(dy)/(ds)=2sln2$

Multiply both sides by $y$

$(dy)/(ds)=2ysln2$

Remember that $y=2^(s^2)$ Therefore

$(dy)/(ds)=2(2^(s^2))sln2$

What is the derivative of y=2^(s^2)y=2^(s^2)?