Q1 (3xy-y3)X5x2-4xy2)
Answers
Answer:
Differentiate the equation from the left and right
15
x
2
(
1
)
=
−
3
x
y
'
+
−
3
y
The product rule was used on -3xy
15
x
2
+
3
y
=
−
3
x
y
'
Divide the -3x over to the other side
−
5
x
−
y
x
=
y
'
The answer.
For -3xy the product rule states f g' + f' g
Say -3x is f and y is g
-3x y' + -3 y
When you differentiate, especially implicit differentiation, you follow what the rules say, and this one is saying
d
y
d
x
.
a
d
x
d
x
causes a 1 (as seen when I did it on the
5
x
3
), and a
d
y
d
x
will cause a y'. For other problems a
d
x
d
y
will cause a x' and the
d
y
d
y
will cause a 1.
Answer:
3x + 7x = (3 + 7) x = 10x
(ii) -5xy + 9xy = (-5 + 9)xy = 4xy
Question: 2
Simplify each of the following:
(i) 7x3y +9yx3
(ii) 12a2b + 3ba2
Solution:
Simplifying the given expressions, we have
(i) 7x3y + 9yx3 = (7 + 9)x3y = 16x3y
(ii) 12a2b + 3ba2 = (12 + 3)a2b =15a2b
Step-by-step explanation:
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