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How do you differentiate #y=3^sinx#?

Answer 1

Scarlett Allison

#y = 3^sinx#

#lny = ln(3^(sinx))#

#lny = sinxln3#

#1/y(dy/dx) = (cosx xx ln3 + 0 xx sinx)#

#dy/dx = (ln3cosx)/(1/y)#

#dy/dx = y xx ln3cosx#

#dy/dx = 3^sinx xx ln3cosx#

#dy/dx = 3^sinxln3cosx#

Hopefully this helps!

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Answer 2

Charles Arocha

The derivative of ( y = 3^{\sin(x)} ) is ( y' = 3^{\sin(x)} \cdot \ln(3) \cdot \cos(x) ).

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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.

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