Question

AJUDEM POR FAVOR, QUEM SOUBER!

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Answer 1

Pela regra do expoente e regra da cadeia:

1)
$y=\sqrt{x+7}\\\\y=(x+7)^\frac{1}{2}\\\\y^\prime=\dfrac{1}{2}(x+7)^{\frac{1}{2}-1}\\\\y^\prime=\dfrac{1}{2}(x+7)^{-\frac{1}{2}}\\\\y^\prime=\dfrac{1}{2}\cdot\dfrac{1}{\sqrt{x+7}}\\\\\boxed{y^\prime=\dfrac{1}{2\sqrt{x+7}}}$


3)
$y=(x^2+1)\cos x\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \boxed{(fg)'=f'g+fg'}\\\\\boxed{y'=2x\cos x+(x^2+1)(-\sin x)}$


As outras duas envolvem vários teoremas.