Free Printable Implicit Differentiation Practice Part 2

1.

Find dy/dx if $3x^2+6y^2+10=5x+7y$

a)

$\frac{dy}{dx}=\frac{-6x+5}{12y-7}$

b)

$\frac{dy}{dx}=\frac{-6x+5}{-12y+7}$

c)

$\frac{dy}{dx}=\frac{6x-5}{12y-7}$

d)

$\frac{dy}{dx}=\frac{-3x+5}{6y-7}$

e)

$\frac{dy}{dx}=\frac{3x-5}{6y-7}$

2.

Differentiate w.r.t x,

12x+6y^2=4x^2+10y

a)

$\frac{dy}{dx}=\frac{2\left(2x-3\right)}{6y-5}$

b)

$\frac{dy}{dx}=\frac{-2\left(2x-3\right)}{6y-5}$

c)

$\frac{dy}{dx}=\frac{\left(2x-3\right)}{6y-5}$

d)

$\frac{dy}{dx}=\frac{-8x+12}{12y-10}$

e)

$\frac{dy}{dx}=\frac{-8x+12}{6y-5}$

3.

Find dy/dx if

y=10x^2+15y=-5y^2-40x

a)

$\frac{dy}{dx}=-\frac{4\left(x+2\right)}{2y+3}$

b)

$\frac{dy}{dx}=\frac{4\left(x+2\right)}{2y+3}$

c)

$\frac{dy}{dx}=\frac{-4x+2}{2y+3}$

4.

What is dy/dx if

5x^2y^3\ =\ 12

a)

$\frac{dy}{dx}=-\frac{2y}{3x}$

b)

$\frac{dy}{dx}=-\frac{2x}{3y}$

c)

$\frac{dy}{dx}=\frac{2y}{3x}$

d)

$\frac{dy}{dx}=-\frac{3x}{2y}$

5.

What is dy/dx if

2x^7y^4=10

a)

$\frac{dy}{dx}=-\frac{7y}{4x}$

b)

$\frac{dy}{dx}=-\frac{7x}{4y}$

c)

$\frac{dy}{dx}=-\frac{4x}{7y}$

d)

$\frac{dy}{dx}=-\frac{14y}{4x}$

e)

$\frac{dy}{dx}=\frac{7y}{4x}$

6.

Find dy/dx if

5x^3+2x^4y^2=10

a)

$\frac{dy}{dx}=\frac{-8x^3y^2-15x^2}{4x^4y}$

b)

$\frac{dy}{dx}=\frac{8x^3y^2+15x^2}{4x^4y}$

c)

$\frac{dy}{dx}=\frac{16x^3y^2-15x^2}{4x^4y}$

d)

$\frac{dy}{dx}=-\frac{4x^2y}{8xy^2+15}$

7.

Find dy/dx if

2x^4y^2-y^3=7

a)

$\frac{dy}{dx}=-\frac{8x^3y^2}{4x^4y-3y^2}$

b)

$\frac{dy}{dx}=\frac{8x^3y^2}{4x^4y-3y^2}$

c)

$\frac{dy}{dx}=\frac{8x^3y^2}{4x^4y+3y^2}$

d)

$\frac{dy}{dx}=-\frac{10x^3y^2}{3x^4y-4y^2}$

8.

Find dy/dx if 8xy = 12

a)

$\frac{dy}{dx}=-\frac{y}{x}$

b)

$\frac{dy}{dx}=\frac{y}{x}$

c)

$\frac{dy}{dx}=-\frac{x}{y}$

d)

$\frac{dy}{dx}=\frac{x}{y}$

9.

Find d/dx if $2x^4y^4=20$

a)

$\frac{dy}{dx}=-\frac{y}{x}$

b)

$\frac{dy}{dx}=\frac{y}{x}$

c)

$\frac{dy}{dx}=-\frac{y^3}{x^3}$

d)

$\frac{dy}{dx}=\frac{y^3}{x^3}$

10.

$-3\sin x+4\cos y=10$

Differentiate w.r.t x

a)

$\frac{dy}{dx}=-\frac{3\cos\left(x\right)}{4\sin\left(y\right)}$

b)

$\frac{dy}{dx}=\frac{3\cos\left(x\right)}{4\sin\left(y\right)}$

c)

$\frac{dy}{dx}=-\frac{3\cos\left(y\right)}{4\sin\left(x\right)}$

d)

$\frac{dy}{dx}=\frac{3\cos\left(y\right)}{4\sin\left(x\right)}$

11.

Find dy/dx if $8\sin y+11\cos x=13$

a)

$\frac{dy}{dx}=\frac{11\sin\left(x\right)}{8\cos\left(y\right)}$

b)

$\frac{dy}{dx}=-\frac{11\sin\left(x\right)}{8\cos\left(y\right)}$

c)

$\frac{dy}{dx}=-\frac{11\cos\left(x\right)}{8\sin\left(y\right)}$

d)

$\frac{dy}{dx}=\frac{11\sin\left(y\right)}{8\cos\left(x\right)}$

12.

Differentiate w.r.t x if

4x^2y^3+3x^4y^5=10

a)

$\frac{dy}{dx}=\frac{-12x^3y^5-8xy^3}{15x^4y^4+12x^2y^2}$

b)

$\frac{dy}{dx}=\frac{12x^3y^5+8xy^3}{15x^4y^4+12x^2y^2}$

c)

$\frac{dy}{dx}=\frac{-24x^4y^6-12xy^2}{15x^5y^3+12x^3y^3}$

d)

$\frac{dy}{dx}=\frac{24x^4y^6+12xy^2}{15x^5y^3-12x^3y^3}$

Implicit Differentiation Practice Part 2

Total questions: 12

Worksheet time: 3hrs 0mins

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