Question

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

Answer 1

is it
\[ \cos\left(\frac{x}{y} \right) - e^{x^2} = \sqrt{y + \log_7 5} \]
?

Answer 2

\[\cos \left( \frac{ x }{ y } \right)\] requires chain and quotient rule

Answer 3

\[\frac{ d }{ dx } \cos\left( \frac{ x }{ y } \right) = -\sin \left( \frac{ x }{ y } \right) \times \left( \frac{ x }{ y } \right)'\] and I think the rest should be pretty simple mhm, I would like to see an attempt.

Answer 4

Also this may come in handy \[\frac{ d }{ dx } \log_a x = \frac{ 1 }{ x \ln a }\]

Answer 5

@phi only the y is under the radical

Answer 6

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

\(\large \frac{d}{dx} cos(\frac{x}{y})=−sin(\frac{x}{y}) .\frac{d}{dx}(\frac{x}{y})\)

Answer 7

**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"

Answer 8

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