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$1$. If $y=x \sin x$, then $\frac{d y}{d x}=$$\newline$(A) $\sin x+\cos x$$\newline$(B) $\sin x+x \cos x$$\newline$(C) $\sin x-x \cos x$$\newline$(D) $x(\sin x+\cos x)$$\newline$(E) $x(\sin x-\cos x)$$\newline$$2$. Let $f$ be the function given by $f(x)=300 x-x^{3}$. On which of the following intervals is the function $f$ increasing?$\newline$(A) $\frac{d y}{d x}=$$0$ and $\frac{d y}{d x}=$$1$$\newline$(B) $\frac{d y}{d x}=$$2$$\newline$(C) $\frac{d y}{d x}=$$3$ only$\newline$(D) $\frac{d y}{d x}=$$4$ only$\newline$(E) $\frac{d y}{d x}=$$5$$\newline$Unauthorized copying or reuse of$\newline$any part of this page is illegal.$\newline$GO ON TO THE NEXT PAGE.$\newline$$\frac{d y}{d x}=$$6$$\newline$A A A A A A A A A A A A A A A A A A A A A A A A A A A A$\newline$$3$. $\frac{d y}{d x}=$$7$$\newline$(A) $\frac{d y}{d x}=$$8$$\newline$(B) $\frac{d y}{d x}=$$9$$\newline$(C) $\sin x+\cos x$$0$$\newline$(D) $\sin x+\cos x$$1$$\newline$(E) $\sin x+\cos x$$2$