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#