Free Printable implicit differentiation

1.

Find the derivative of $y=\left(x+1\right)^x$ .

a)

$\frac{dy}{dx}=\frac{1}{x+1}$

b)

$\frac{dy}{dx}=\left(x+1\right)^x\left(\ln\left(x+1\right)+\frac{x}{x+1}\right)$

c)

$\frac{dy}{dx}=x\left(x+1\right)^{x-1}$

d)

$\frac{dy}{dx}=\ln\left(x+1\right)+\frac{x}{x+1}$

2.

Use implicit differentiation to find $\frac{dy}{dx}$ of $5x^2-4y^2=9$ at the point $\left(x,y\right)=\left(2,3\right)$ .

a)

$0$

b)

$\frac{5}{2}$

c)

$9$

d)

$\frac{5}{6}$

3.

Find $\frac{d^{10}}{dx^{10}}\ln\left(2x\right)$ .

a)

$-\frac{3628800}{x^{10}}$

b)

$-\frac{362880}{x^{10}}$

c)

$\frac{362880}{x^{10}}$

d)

$-\frac{362880}{x^9}$

4.

Find the point for which the graph of $y=\left[\ln\left(x+4\right)\right]^2$ has a horizontal tangent line.

a)

$\left(-3,0\right)$

b)

$\left(0,\left(\ln4\right)^2\right)$

c)

$\left(2,\left(\ln6\right)^2\right)$

d)

$\left(0,0\right)$

5.

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

a)

6 -x

b)

3x² +3y²

c)

−x²/y²

d)

0

6.

Find dy/dx by Implicit Differentiation
xy = 6

a)

-x/ y

b)

-y/ x

c)

-6y/ x

d)

y/x

7.

Find dy/dx
xy+y²=2

a)

-y/(x+2y)

b)

y/(x+2y)

c)

-3y/x

d)

-3x/y

8.

a)

-2

b)

-2/3

c)

2/3

d)

2

9.

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)

10.

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

11.

Which of the following equations, if any, are written in implicit form?

(Check all that apply)

a)

$y=4\ x-9$

b)

$x^{\ 2}+y^{\ 2}=49$

c)

$x\ y=16$

d)

$y=\sqrt{36-x^{\ 2}}$

e)

$y=\frac{25\ x}{x^{\ 2}-64}$

12.

Using Implicit Differentiation, find $\frac{\text{d}y}{\text{d}x}$ for $\sin\ \left(x^2y^2\right)=x$

a)

$\frac{1}{2x^2y\ \cos\left(x^2y^2\right)}-\frac{2y}{x}$

b)

$\frac{2}{2x^2y^2\cos\ \left(x^2y^2\right)}-\frac{y}{x}$

c)

$\frac{1}{2x^2y\cos\left(x^2y^2\right)}-\frac{y}{x}$

13.

Find dy/dx by Implicit Differentiation
2xy³- x²y = 2

a)

2xy - 2y³

b)

2y(x-y²)/x(6y²-x)

c)

-2y/x

d)

2

14.

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)

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

15.

Using Implicit Differentiation, find $\frac{\text{d}y}{\text{d}x}$ for $\sin\ \left(x^2y^2\right)=x$

a)

$\frac{1}{2x^2y\ \cos\left(x^2y^2\right)}-\frac{2y}{x}$

b)

$\frac{2}{2x^2y^2\cos\ \left(x^2y^2\right)}-\frac{y}{x}$

c)

$\frac{1}{2x^2y\cos\left(x^2y^2\right)}-\frac{y}{x}$

implicit differentiation

Total questions: 15

Worksheet time: 1hrs 12mins

Similar Resources on Wayground