Implicit and parametric differentiation Quiz

1. Differentiate $y^{3}$ with respect to $x$.

• A. $3y^{2}\frac{dy}{dx}$
• B. $3y^{2}$
• C. $y^{3}\frac{dy}{dx}$
• D. $3x^{2}$

2. Differentiate $x^{2}y$ with respect to $x$.

• A. $2x\frac{dy}{dx}$
• B. $x^{2}\frac{dy}{dx}$
• C. $2xy$
• D. $2xy+x^{2}\frac{dy}{dx}$

3. A curve has $x=2t$, $y=t^{2}$. Find $\frac{dy}{dx}$.

• A. $2t$
• B. $t$
• C. $\frac1t$
• D. $4t$

4. On $x^{2}+y^{2}=25$, find the gradient at $(3,4)$.

• A. $\frac34$
• B. $\frac43$
• C. $-\frac34$
• D. $-\frac43$

5. A curve has $x=t^{2}$, $y=2t$. Find the gradient of the normal at $t=2$.

• A. $\frac12$
• B. $2$
• C. $-\frac12$
• D. $-2$