$f(x)=\cos x$ এবং $g(x)=x \sqrt{1+y}+y \sqrt{1+x}$ যেখানে $x \neq y$

Consider the following statements in respect of the function $f(x) = x^{3} - 1, \quad x\epsilon [-1, 1]$

I. $f(x)$ is increasing in $[-1, 1]$

II. $f'(x)$ has no root in $(-1, 1)$.

Which of the statements given above is/ are correct?

If $2^x+2^y=2^{x+y}$, then $\displaystyle \frac {dy}{dx}$ has the value equal to

যদি $e^{x y+1}=6$ হয়, তবে $\frac{d y}{d x}=$ কত?