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ADDMATH F5 CHP 2 DIFFERENTIATION

Total questions: 32

Worksheet time: 35mins

Name
Class
Date
1.

Evaluate the following limit:

lim⁡x→2(3x+7−4x2)\lim_{x\rightarrow2}\left(3x+7-4x^2\right)

a)

−3-3

b)

33

c)

29

d)

-29

2.

Choose CORRECT statement(s):

lim⁡x→6(x2−36x−6)\lim_{x\rightarrow6}\left(\frac{x^2-36}{x-6}\right)

a)

undefined

b)

lim⁡x→6(x+6)\lim_{x\rightarrow6}\left(x+6\right)

c)

10

d)

00\frac{0}{0}

3.

Differentiate the following by using first principle method:

f(x)=5x−3f\left(x\right)=5x-3

Choose CORRECT statements.

a)

f(x+h)=5x+5h−3f\left(x+h\right)=5x+5h-3

b)

lim⁡h→0(5x+5h−3−5x+3h)\lim_{h\rightarrow0}\left(\frac{5x+5h-3-5x+3}{h}\right)

c)

lim⁡h→0(5h)\lim_{h\rightarrow0}\left(5h\right)

d)

f′(x)=5f'\left(x\right)=5

4.

Find dydx\frac{dy}{dx} of the following function:

y=9y=9

a)

9x+c9x+c

b)

99

c)

00

d)

11

5.

Find dydx\frac{dy}{dx} of the following function:

y=3x+2y=3x+2

a)

3x22+c\frac{3x^2}{2}+c

b)

33

c)

22

d)

55

6.

Find dydx\frac{dy}{dx} of the following function:

y=6x2+2x+2y=6x^2+2x+2

a)

12x+212x+2

b)

2x3+x2+2x2x^3+x^2+2x

c)

22

d)

12x12x

7.

If dydx=2x+4\frac{dy}{dx}=2x+4 , then y=?y=?

a)

x2+4xx^2+4x

b)

x2+4x+4x^2+4x+4

c)

2x2+8x2\frac{2x^2+8x}{2}

d)

22

8.

Find ddx(2 x)\frac{d}{dx}\left(2\ \sqrt[]{x}\right) .

a)

1x\frac{1}{\sqrt[]{x}}

b)

x\sqrt[]{x}

c)

43x32\frac{4}{3}x^{\frac{3}{2}}

d)

2x2x

9.

Differentiate the following: y=1x2y=\frac{1}{x^2} .

a)

−2x3-\frac{2}{x^3}

b)

−1x-\frac{1}{x}

c)

1x3\frac{1}{x^3}

d)

12x\frac{1}{2x}

10.

Differentiate the following with respect to x:

f(x)=(x−1)(2x+3)f\left(x\right)=\left(x-1\right)\left(2x+3\right)

a)

2x2+x−32x^2+x-3

b)

4x+14x+1

c)

22

d)

00

11.

Differentiate the following:

y=(x−5)2y=\left(x-5\right)^2

a)

x2−10x+25x^2-10x+25

b)

2x−102x-10

c)

x−5x-5

d)

11

12.

Find d2ydx2\frac{d^2y}{dx^2} the following function:

y=10x3−3x2+3xy=10x^3-3x^2+3x

a)

30x2−6x+330x^2-6x+3

b)

60x−660x-6

13.

Choose CORRECT statements for the following question:

Find f′(x)f'\left(x\right) for f(x)=x2(x−3)5f\left(x\right)=x^2\left(x-3\right)^5 .

a)

Let u=x2 and v=(x−3)2Let\ u=x^2\ and\ v=\left(x-3\right)^2

b)

v ′=5(x−3)4(1)v\ '=5\left(x-3\right)^4\left(1\right) =5(x−3)4=5\left(x-3\right)^4

c)

f′(x)=5x2(x−3)4+2x(x−3)5f'\left(x\right)=5x^2\left(x-3\right)^4+2x\left(x-3\right)^5

d)

f′(x)=x(x−3)4(7x−6)f'\left(x\right)=x\left(x-3\right)^4\left(7x-6\right)

14.

Choose CORRECT statements for the following question:

Find f′(x)f'\left(x\right) for f(x)=x+11−2xf\left(x\right)=\frac{x+1}{1-2x} .

a)

Let u=x+1  and  v=1−2xLet\ u=x+1\ \ and\ \ v=1-2x

b)

u′=1u'=1

c)

f′(x)=−3(1−2x)2f'\left(x\right)=\frac{-3}{\left(1-2x\right)^2}

d)

v ′ =2v\ '\ =2

15.

For the following function:

y=e5xy=e^{5x}

Choose CORRECT statements

a)

dydx=5e5x\frac{dy}{dx}=5e^{5x}

b)

d2ydx2=25e5x\frac{d^2y}{dx^2}=25e^{5x}

c)

dydx=15e5x\frac{dy}{dx}=\frac{1}{5}e^{5x}

d)

dydx=e5x\frac{dy}{dx}=e^{5x}

16.

Find ddx(1e2x)\frac{d}{dx}\left(\frac{1}{e^{2x}}\right) .

a)

−2e2x-\frac{2}{e^{2x}}

b)

2e2x\frac{2}{e^{2x}}

c)

12e2x\frac{1}{2e^{2x}}

d)

2e2x2e^{2x}

17.

Differentiate the following function:

y=exy=\sqrt[]{e^x}

a)

1ex\frac{1}{\sqrt[]{e^x}}

b)

2 ex  2\ \sqrt[\ \ ]{e^x}

c)

ex2\frac{\sqrt[]{e^x}}{2}

18.

Differentiate the following function:

y=ln⁡(3+4x)y=\ln\left(3+4x\right)

a)

43+4x\frac{4}{3+4x}

b)

4ln⁡(3+4x)4\ln\left(3+4x\right)

c)

14(3+4x)\frac{1}{4\left(3+4x\right)}

19.

Differentiate the following function:

y=ln⁡(3x+1)2y=\ln\left(3x+1\right)^2

Choose CORRECT statements

a)

y=2ln⁡(3x+1)y=2\ln\left(3x+1\right)

b)

dydx=2[33x+1]\frac{dy}{dx}=2\left[\frac{3}{3x+1}\right]

c)

dydx=63x+1\frac{dy}{dx}=\frac{6}{3x+1}

d)

32(3x+1)\frac{3}{2\left(3x+1\right)}

20.

Differentiate the following function:

y=ln⁡x2+1y=\ln\sqrt[]{x^2+1}

Choose CORRECT statements.

a)

y=12ln⁡(x2+1)y=\frac{1}{2}\ln\left(x^2+1\right)

b)

dydx=12[2xx2+1]\frac{dy}{dx}=\frac{1}{2}\left[\frac{2x}{x^2+1}\right]

c)

dydx=2xx2+1\frac{dy}{dx}=\frac{2x}{x^2+1}

d)

dydx=xx2+1\frac{dy}{dx}=\frac{x}{x^2+1}

21.

Bezakan

f(x)=x5(3x−2)f\left(x\right)=x^5\left(3x-2\right)  

a)

f′(x)=18x5f'\left(x\right)=18x^5  

b)

f′(x)=8x4f'\left(x\right)=8x^4  

c)

f′(x)=18x5−10x4f'\left(x\right)=18x^5-10x^4  

d)

f′(x)=8x5−5x4f'\left(x\right)=8x^5-5x^4  

22.

Bezakan ungkapan berikut terhadap x.


2x2+3x+5.

a)

4x

b)

4x2

c)

3

d)

4x+3

23.

Cari terbitan pertama fungsi berikut

f(x) = x3 + x2 + 3

a)

3x2 + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x3 + x2

24.

Bezakan

f(x) = 7

a)

7

b)

0

c)

7x

d)

14

25.

Jika f(x)=3x23+6x−13f\left(x\right)=3x^{\frac{2}{3}}+6x^{-\frac{1}{3}}  , cari nilai bagi  f′(8)f'\left(8\right) . 


a)

87\frac{8}{7}  

b)

−78-\frac{7}{8}  

c)

−78-\frac{7}{8}  

d)

78\frac{7}{8}  

26.

Bezakan

6x236x^{\frac{2}{3}}  

a)

4x−134x^{-\frac{1}{3}}  

b)

4x−234x^{-\frac{2}{3}}

c)

6x136x^{\frac{1}{3}}  

d)

4x134x^{\frac{1}{3}}

27.

y=14x−6y=\frac{1}{4}x^{-6}  
Cari terbitan pertama bagi fungsi di atas:
Sila pilih dua jawapan sahaja

a)

dydx=6(14x)−6−1\frac{dy}{dx}=6\left(\frac{1}{4}x\right)^{-6-1}  

b)

dydx=−6(14x)−6−1\frac{dy}{dx}=-6\left(\frac{1}{4}x\right)^{-6-1}  

c)

dydx=−32x−7\frac{dy}{dx}=-\frac{3}{2}x^{-7}  

d)

dydx=32x7\frac{dy}{dx}=\frac{3}{2}x^7  

28.

Cari  dydx\frac{dy}{dx}  
y=12x−3y=12x^{-3}  

a)

dydx=−36x−2\frac{dy}{dx}=-36x^{-2}  

b)

dydx=−36x−4\frac{dy}{dx}=-36x^{-4}  

c)

dydx=36x−2\frac{dy}{dx}=36x^{-2}  

d)

dydx=36x−3\frac{dy}{dx}=36x^{-3}  

29.

Cari nilai bagi had berikut  hadx→1 x3−xx−1had_{x\rightarrow1}\ \frac{x^3-x}{x-1}  

a)

2

b)

0 

c)

-2

d)

-1

30.

y=−5x4+2x3y=-5x^4+2x^3  

Bezakan fungsi di atas :

a)

dydx=−20x3+6x2\frac{dy}{dx}=-20x^3+6x^2  

b)

dydx=20x3+6x\frac{dy}{dx}=20x^3+6x  

c)

dydx=−20x3+3x2\frac{dy}{dx}=-20x^3+3x^2  

d)

dydx=−20x3+6x\frac{dy}{dx}=-20x^3+6x  

31.
Diberi f(x)=2(1-5x)⁻⁴, cari f'(x).
a)
40(1-5x)⁻⁵
b)
-8(1-5x)⁻³
c)
-8(1-5x)⁻⁵
d)
40(1-5x)⁻³
32.

Cari nilai bagi

dydx\frac{\text{d}y}{\text{d}x}  bagi fungsi berikut  f(x)=(2x+5)4f\left(x\right)=\left(2x+5\right)^4  apabila  x=1x=1  

a)

2477

b)

2744

c)

2747

d)

2474