2.3. Techniques of Differentiation http://www.ck12.org
6.y= (x^3 − 3 x^2 +x)( 2 x^3 + 7 x^4 )
7.y= (^1 x+x^12 )( 3 x^4 − 7 )
8.y=√x+√^1 x
9.y=√^3 x+ 3
10.y=^4 x 2 x+−^19- Newton’s Law of Universal Gravitation states that the gravitational force between two masses (say, the earth
and the moon),mandM, is equal to their product divided by the square of the distancerbetween them.
Mathematically,
F=GmMr 2 ,whereGis the Universal Gravitational Constant(
1. 602 × 10 −^11 Nmkg 22)
. If the distancerbetween the two
masses is changing, find a formula for the instantaneous rate of change ofFwith respect to the separation
distancer.
12. Find
d
dψ
[ψψ
0 +ψ^3
3 −ψ 0]
whereψ 0 is a constant.- Findddx^3 y 3
∣∣
∣x= 1 , wherey=x^23.