$$ \text { If } \sin y=x(\cos (a+y)) \text {, then find } \frac{d y}{d x} \text { when } x=0 $$

The approximate value of $$f(5.001)$$, where $$f(x)=x^3-7 x^2+10$$

$$ \text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to } $$

If $$f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}$$ then the value of $$f^{\prime}(0)$$ is equal to