Free Printable IMPLICIT AND PARAMETRIC DIFFERENTIATION

1.

Find dy/dx by Implicit Differentiation
x³ +y³ = 36

a)

6 -x

b)

3x² +3y²

c)

−x²/y²

d)

0

2.

Find dy/dx
xy+y²=2

a)

-y/(x+2y)

b)

y/(x+2y)

c)

-3y/x

d)

-3x/y

3.

Find the derivative:
y=5x²e^3x

a)

y'=10xe^3x(2x+3)

b)

y'=5xe^3x(3x+2)

c)

y'=10ex^3x(3x+2)

d)

y'=5xe^3x(2x+3)

4.

Find the second derivative of f(x) = x²+ e^x - cosx

a)

f"(x) = 2 + e^x + cosx

b)

f"(x) = 2x + e^x + cosx

c)

f"(x) = 2x + xe^x - cosx

d)

f"(x) = 2x + e^x + sinx

5.

Find dy/dx at the given point

x³ +2xy -y²=11 at (2,3)

a)

-4/7

b)

12

c)

-9

d)

9

6.

Find $\frac{dy}{dx}$ : $2x^2-3y^2=4$

a)

$\frac{2x}{y}$

b)

$\frac{x}{3y}$

c)

$\frac{3y}{2x}$

d)

$\frac{2x}{3y}$

7.

Find the derivative of $x^2+xy+y^3=0$

a)

$-\ \frac{2x}{1+3y^2}$

b)

$-\frac{x+3y^2}{2x+y}$

c)

$-\frac{2x+y}{x+3y^2}$

d)

$-\frac{2x}{x+3y^2}$

8.

Find the point based on the parametric equations. t = 3

x = 1 - 2t

y =4t + 1

a)

(-5, 13)

b)

(13, -5)

c)

(5, 13)

d)

(13, 5)

9.

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

a)

(2, 4)

b)

(4, 2)

c)

(-6, 0)

d)

(0,-6)

10.

For $x=3t^2+1,\ y=t^3-2t^2$ , determine $\frac{d^2y}{dx^2}$ in terms of t.

a)

$\frac{d^2y}{dx^2}=-\frac{1}{12t}$

b)

$\frac{d^2y}{dx^2}=\frac{1}{12}$

c)

$\frac{d^2y}{dx^2}=\frac{1}{12t}$

d)

$\frac{d^2y}{dx^2}=-\frac{1}{t}$

11.

For $x=\frac{1}{2}t^2+2,\ y=\sin\left(t+1\right)$ , determine $\frac{d^2y}{dx^2}$ in terms of t.

a)

$\frac{d^2y}{dx^2}=\frac{t\cos\left(t+1\right)+\sin\left(t+1\right)}{t^3}$

b)

$\frac{d^2y}{dx^2}=\frac{-t\cos\left(t+1\right)-\sin\left(t+1\right)}{t^3}$

c)

$\frac{d^2y}{dx^2}=\frac{t\sin\left(t+1\right)+\cos\left(t+1\right)}{t^3}$

d)

$\frac{d^2y}{dx^2}=\frac{-t\sin\left(t+1\right)-\cos\left(t+1\right)}{t^3}$

12.

For $x=e^{-t},\ y=t^3+t+1$ , determine $\frac{d^2y}{dx^2}$ in terms of t.

a)

$\frac{d^2y}{dx^2}=\left(3t^2+6t+1\right)e^{2t}$

b)

$\frac{d^2y}{dx^2}=\left(t^2+6t+1\right)e^{2t}$

c)

$\frac{d^2y}{dx^2}=\left(3t^2+6t+1\right)e^t$

d)

$\frac{d^2y}{dx^2}=\left(t^2+t+1\right)e^{2t}$

IMPLICIT AND PARAMETRIC DIFFERENTIATION

Total questions: 12

Worksheet time: 44mins

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