If y = (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)(1 + x¹⁶) then what is $\frac{dy}{dx}$ at x = 0 equal to?

If y = cos x ⋅ cos 4x ⋅ cos 8x, then what is $\rm \frac{1}{y}\frac{dy}{dx}$ at $\rm x = \frac{\pi}{4}$ equal to?

Let f(x) be a polynomial function such that f ∘ f(x) = x⁴. What is f'(1) equal to ?

What is the derivative of $\rm e^{e^x}$ with respect to e^x?