Differentiating powers of x Quiz

1. Differentiate $3x^4-2x$ with respect to $x$.

• A. $12x^3$
• B. $3x^3-2$
• C. $12x^3-2$
• D. $12x^4-2x$

2. Differentiate $\frac{4}{\sqrt{x}}$.

• A. $-2x^{-\frac32}$
• B. $2x^{-\frac12}$
• C. $-4x^{-\frac32}$
• D. $-\frac{2}{x^{\frac12}}$

3. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ when $y=x+\frac{1}{x}$.

• A. $1+x^{-2}$
• B. $1-x^{-1}$
• C. $x-x^{-2}$
• D. $1-x^{-2}$

4. Find the gradient of $y=x^{\frac32}$ at $x=4$.

• A. $2$
• B. $3$
• C. $\frac{3}{4}$
• D. $12$

5. Find $\frac{\mathrm{d}y}{\mathrm{d}x}$ when $y=(2x-1)^2$.

• A. $2(2x-1)$
• B. $4x-2$
• C. $8x-4$
• D. $4x^2-4x+1$