Product, quotient and chain rules Quiz

1. Differentiate $y=(3x^2-1)^4$.

• A. $4(3x^2-1)^3$
• B. $24x(3x^2-1)^3$
• C. $12x(3x^2-1)^3$
• D. $(6x)^4$

2. Differentiate $y=x\sin2x$.

• A. $\sin2x+2x\cos2x$
• B. $\cos2x$
• C. $\sin2x+x\cos2x$
• D. $2\cos2x$

3. Differentiate $y=\frac{e^{x}}{x}$.

• A. $\frac{e^{x}}{1}$
• B. $\frac{e^{x}(1+x)}{x^2}$
• C. $\frac{e^{x}(x-1)}{x}$
• D. $\frac{e^{x}(x-1)}{x^2}$

4. A sphere has $V=\frac43\pi r^3$ and $\frac{dV}{dt}=36$ cm$^3$ s$^{-1}$. Find $\frac{dr}{dt}$ when $r=3$.

• A. $\frac{1}{\pi}$ cm s$^{-1}$
• B. $\pi$ cm s$^{-1}$
• C. $1$ cm s$^{-1}$
• D. $36\pi$ cm s$^{-1}$

5. If $x=y^3+y$, find $\frac{dy}{dx}$ when $y=1$.

• A. $4$
• B. $\frac13$
• C. $\frac14$
• D. $\frac15$