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

Answer 1

Scarlett Allison

#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#

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Answer 2

Christopher Agresta

To find the derivative of ( y = 2^{s^2} ), we use the chain rule. The derivative is ( \frac{dy}{ds} = 2^{s^2} \cdot 2s \cdot \ln(2) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.