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PhoenixFire
 2 years ago
find dy/dx of y=(sin(x))^x
PhoenixFire
 2 years ago
find dy/dx of y=(sin(x))^x

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lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1ln both sides \[\ln y = x \ln (\sin x)\] do implicit differentiation yada yada...got it?

PhoenixFire
 2 years ago
Best ResponseYou've already chosen the best response.0Yup. Makes sense. thanks.

lgbasallote
 2 years ago
Best ResponseYou've already chosen the best response.1so can you do it from here?

PhoenixFire
 2 years ago
Best ResponseYou've already chosen the best response.0Yes I can... forgot about implicit. Should be good.

beeqay
 2 years ago
Best ResponseYou've already chosen the best response.0Phoenix, do you know why we use log differentiation here?

beeqay
 2 years ago
Best ResponseYou've already chosen the best response.0Phoenix, do you know why we use log differentiation here?

beeqay
 2 years ago
Best ResponseYou've already chosen the best response.0This would be helpful for the future. \[d/dx (a^b) = 0\] because a and b are just constants. \[d/dx (x^n) = nx^{n1}\] \[d/dx (f(x)^{g(x)}= \log differentiation\] because it's a function raised to a function.

beeqay
 2 years ago
Best ResponseYou've already chosen the best response.0n is a constant in the second case.

PhoenixFire
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks beeqay. Helpful to know that.
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