Answer:
6(6a-2b)
Step-by-step explanation:
The picture is not clear. let me assume
y = (x^4)ln(x^3)
product rule :
d f(x)g(x) = f(x) dg(x) + g(x) df(x)
dy/dx = (x^4)d[ln(x^3)/dx] + d[(x^4)/dx] ln(x^3)
= (x^4)d[ln(x^3)/dx] + 4(x^3) ln(x^3)
look at d[ln(x^3)/dx]
d[ln(x^3)/dx]
= d[ln(x^3)/dx][d(x^3)/d(x^3)]
= d[ln(x^3)/d(x^3)][d(x^3)/dx]
= [1/(x^3)][3x^2] = 3/x
... chain rule (in detail)
end up with
dy/dx = (x^4)[3/x] + 4(x^3) ln(x^3)
= x^3[3 + 4ln(x^3)]
Answer:
search-icon-header
Search for questions & chapters
search-icon-image
Question
Bookmark
A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If the diameter of the wheel is 60cm, calculate the speed per hour with which the boy is cycling.
Easy
Solution
verified
Verified by Toppr
Radius of the wheel =r=
2
60
=30 cm
Circumference of the wheel =2πr=2×
7
22
×30=
7
1320
cm
Distance covered in 1 revolution =
7
1320
cm
Distance covered in 140 revolutions =
7
1320
×140=26400 cm=264 m=
1000
264
km
Distance covered in one minute = Distance covered in 140 revolutions =
1000
264
km
Distance covered in 1 hour =
1000
264
×60=15.84 km
Hence, the speed with which the boy is cycling is 15.84km/hr.
