Implicit and parametric differentiation Quiz

1. Differentiate $x^2+y^2=25$ implicitly to find $\frac{dy}{dx}$.

• A. $\frac xy$
• B. $-\frac yx$
• C. $-\frac xy$
• D. $\frac yx$

2. Find $\frac{dy}{dx}$ for $x^2y=4$.

• A. $-\frac{2y}{x}$
• B. $-\frac{2x}{y}$
• C. $\frac{2y}{x}$
• D. $-\frac{y}{2x}$

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

• A. $3t$
• B. $\frac{t}{3}$
• C. $\frac{2}{3t}$
• D. $6t^2$

4. A curve has $x=2t+1$ and $y=t^2$. Find the gradient where $t=3$.

• A. $6$
• B. $9$
• C. $1$
• D. $3$

5. The tangent to a curve with gradient $\frac{dy}{dx}=\frac{3-x}{y+2}$ is vertical when...

• A. $x=3$
• B. $y=-2$
• C. $y=2$
• D. $x=-3$