How to find the derivative of cos(x/y)-e^x^2=sqt(y)+log5base7

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How to find the derivative of cos(x/y)-e^x^2=sqt(y)+log5base7

Mathematics
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  • phi
is it \[ \cos\left(\frac{x}{y} \right) - e^{x^2} = \sqrt{y + \log_7 5} \] ?
\[\cos \left( \frac{ x }{ y } \right)\] requires chain and quotient rule
\[\frac{ d }{ dx } \cos\left( \frac{ x }{ y } \right) = -\sin \left( \frac{ x }{ y } \right) \times \left( \frac{ x }{ y } \right)'\] and I think the rest should be pretty simple mhm, I would like to see an attempt.

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Also this may come in handy \[\frac{ d }{ dx } \log_a x = \frac{ 1 }{ x \ln a }\]
@phi only the y is under the radical
so that's : \(\large cos (\frac{x}{y})-e^{x{^2}} = \sqrt{y} + log_75 \) which is now a wee bit easier as the constant at the end goes to zero. so now take it from @Astrophysics steer \(\large \frac{d}{dx} cos(\frac{x}{y})=−sin(\frac{x}{y}) .\frac{d}{dx}(\frac{x}{y})\)
  • phi
**only the y is under the radical*** ok, that is what you posted. But that means the last term (though it looks ugly) is just a constant, and when you take the derivative, it "goes away"
  • phi
You should use "implicit differentiation" on this problem if you need a refresher, try https://www.khanacademy.org/math/differential-calculus/taking-derivatives/implicit_differentiation

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