4. 4
y=(3x+2) , then u=3x+2 and 3
du
dx
=
4
3 3
y=u
=4u 4(3 2)
dy
x
du
= +
3 3dy
= =4(3x+2) 3=12(3x+2)
dx
dy du
du dx
4
Differentiate y=(3x+2)
5. 2
Find the derivative of x +1
1
2 2
y=(x +1)
2
Let u=x +1
du
=2x
dx
1
2
1
-
2
2
1 1
2 2 1
y u
dy
u
du x
=
= =
+
2 2
dy dy du 1 x
= = .2x=
dx du dx 2 x +1 x +1
6. 5
2
2
Differentiate y= , 1.
1
x
with respect to x when x
x
= ÷
+
2
2x
Let u=
x +1 2 2 2 2
2 2 2 2 2 2
du (x +1)(2)-2x(2x) 2x +2-4x 2 2
= =
dx (x +1) (x +1) ( 1)
x
x
−
=
+
5
4
4
2
y=u
dy 2x
=5u =5
du x +1
÷
4 2
2 2 2
dy dy du 2x 2 -2x
= =5
dx du dx x +1 (x +1)
÷ ÷
dy 2
When x=1,then =5 (0)=0
dx 2
÷
7. Differentiate the following exercises
with respect to x:
3
4 5
4
2
1. (1+7x) Leaving CertificateHigher paper1 2005 no6(a)(i)
2. (x 1) Leaving CertificateHigher paper1 2002 no6(a)(i)
3. If y= 3 5, what is ?
2 5
4. If y= , hat is ?
1
5. If y= , hat is
2 5
dy
x
dx
x dy
w
x dx
dy
w
x
+
+
+
÷
÷
+
?
dx
