Let [x] denote the greatest integer function. Then match List-I with List-II:

Choose the correct answer from the options given below.

If $$y = log_{√e}(sin x)$$ then $$\frac{dy}{dx}$$ is :​

Find $$\frac{dy}{dx}$$​ given the following implicit equation: $$x^2+y^2=a^2$$

The derivative of the function $$f(x)=-3x^2+6x-4$$​ is given by:

Differentiate $$f(x)$$​ = cos(tan $$3x$$​) + sin(tan $$3x$$).

Find the value of dy/dx if $$x=cost,y=sint$$​.

If $$x^4+y^4=16$$​, then find the second derivative of $$y$$​.

​$$\text { If } f(x)=\frac{1-x}{2+x} \text {, then find } f^{\prime}(x) \text {. }$$​​

​$$\text { Find the first derivative of } e^{x \ln a}+e^{a \ln x}+e^{a \ln a} \text {. }$$​​

​$$\text { The derivative of } \tan ^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right) \text { with respect to } \tan ^{-1} x \text { is: }$$​​
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If $$y = log_{√e}(sin x)$$ then $$\frac{dy}{dx}$$ is :​