Spm Addmath_differentiation Exercise I
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ONE-SCHOOL.NET Differentiation Exercise I 2. y = x 7
Differentiation of a Constant y=a dy =0 dx
a is a constant
3. y = x111
Example y=2 dy =0 dx
4. y = x −3
Exercise 1 dy Find in the exercise below. dx 1. y = 2
5. y = x −6
6. y = x −1
2. y = 210
3. y =
2 3
1
7. y = x 2
4
4. y = 23
8. y = x 5
Differentiation of a Function I
9. y = x
y = xn
3 14
dy = nx n−1 dx
10. y = x
Example y = x3 dy = 3x 2 dx
11. y = x
Exercise 2 dy in the exercise below. Find dx 1. y = x 2
http://www.one-school.net/notes.html
1
−
1 2
−
2 3
ONE-SCHOOL.NET Differentiation of a Function II
Differentiation of a Function II
y = ax dy = ax1−1 = ax 0 = a dx
y = ax n dy = anx n−1 dx
Example y = 3x dy =3 dx
Example y = 2 x3 dy = 2(3) x 2 = 6 x 2 dx
Exercise 3 Find the f’(x) of the following functions. 1. f ( x) = 6 x
Exercise 4 Differentiate the function below. 1. f ( x) = 6 x 3
2.
f ( x) = −21x
2.
f ( x) = −3 x 6
3.
1 f ( x) = − x 3
3.
f ( x) = 5 x −2
4.
6 f ( x) = x 7
4.
f ( x) =
5.
f ( x) = 25 x
5.
f ( x) = 25 x 5
2 3 x 3
1
http://www.one-school.net/notes.html
2
ONE-SCHOOL.NET Differentiation of a Fraction Function
Additional Notes
1 xn Rewrite
3 x2 y = 3 x −2
y=
y=
y = x−n 1 3x 2 1 y = x −2 3
dy −n = − nx − n−1 = n+1 dx x
y=
Example 1 y= x y = x −1 −1 dy = −1x −2 = 2 dx x
2 3x 2 2 y = x −2 3 y=
Exercise 5 Find the derivative of the function below. 1 1. y = 2 x
2. y =
1 2
x3
http://www.one-school.net/notes.html
3
3. y =
3 x
4. y =
7 x2
ONE-SCHOOL.NET 5. y =
15 x5
1 6 x2
2 x3
9. y =
1 3x 6
1 2 x7
10. y =
2 5x2
6. y = −
7. y =
8. y = −
http://www.one-school.net/notes.html
4
ONE-SCHOOL.NET 11. y = −
12. y =
12 7 x7
2 −9 x 3
2 x6 13. y = −9
http://www.one-school.net/notes.html
5
Differentiation of a Constant y=a dy =0 dx
a is a constant
3. y = x111
Example y=2 dy =0 dx
4. y = x −3
Exercise 1 dy Find in the exercise below. dx 1. y = 2
5. y = x −6
6. y = x −1
2. y = 210
3. y =
2 3
1
7. y = x 2
4
4. y = 23
8. y = x 5
Differentiation of a Function I
9. y = x
y = xn
3 14
dy = nx n−1 dx
10. y = x
Example y = x3 dy = 3x 2 dx
11. y = x
Exercise 2 dy in the exercise below. Find dx 1. y = x 2
http://www.one-school.net/notes.html
1
−
1 2
−
2 3
ONE-SCHOOL.NET Differentiation of a Function II
Differentiation of a Function II
y = ax dy = ax1−1 = ax 0 = a dx
y = ax n dy = anx n−1 dx
Example y = 3x dy =3 dx
Example y = 2 x3 dy = 2(3) x 2 = 6 x 2 dx
Exercise 3 Find the f’(x) of the following functions. 1. f ( x) = 6 x
Exercise 4 Differentiate the function below. 1. f ( x) = 6 x 3
2.
f ( x) = −21x
2.
f ( x) = −3 x 6
3.
1 f ( x) = − x 3
3.
f ( x) = 5 x −2
4.
6 f ( x) = x 7
4.
f ( x) =
5.
f ( x) = 25 x
5.
f ( x) = 25 x 5
2 3 x 3
1
http://www.one-school.net/notes.html
2
ONE-SCHOOL.NET Differentiation of a Fraction Function
Additional Notes
1 xn Rewrite
3 x2 y = 3 x −2
y=
y=
y = x−n 1 3x 2 1 y = x −2 3
dy −n = − nx − n−1 = n+1 dx x
y=
Example 1 y= x y = x −1 −1 dy = −1x −2 = 2 dx x
2 3x 2 2 y = x −2 3 y=
Exercise 5 Find the derivative of the function below. 1 1. y = 2 x
2. y =
1 2
x3
http://www.one-school.net/notes.html
3
3. y =
3 x
4. y =
7 x2
ONE-SCHOOL.NET 5. y =
15 x5
1 6 x2
2 x3
9. y =
1 3x 6
1 2 x7
10. y =
2 5x2
6. y = −
7. y =
8. y = −
http://www.one-school.net/notes.html
4
ONE-SCHOOL.NET 11. y = −
12. y =
12 7 x7
2 −9 x 3
2 x6 13. y = −9
http://www.one-school.net/notes.html
5
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