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How do you differentiate #y= 10^ (tan (pi)(theta)#?

Answer 1

Cameron Alexander

#dy/(dθ) = 10^tan(πθ) (πln(tan(πθ))) /cos^2(πθ)#

Let #v = πθ# and #u = tanv#. Using the chain rule, #dy/(dθ) = dy/(du) (du)/(dv) (dv)/(dθ)#

So now, #y = 10^u#, so:

#dy/(dθ) = 10^u lnu * 1/cos^2(v) * π#

#= 10^tan(πθ) (πln(tan(πθ))) /cos^2(πθ)#

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Answer 2

Emma Aldridge

To differentiate y = 10^(tan(π*θ)) with respect to θ, apply the chain rule:

dy/dθ = 10^(tan(πθ)) * ln(10) * sec^2(πθ) * π.

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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.