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

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1. phi

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

2. Astrophysics

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

3. Astrophysics

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

4. Astrophysics

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

5. elleblythe

@phi only the y is under the radical

6. IrishBoy123

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

7. 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"

8. 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