If you used Clearing in 2024, how did you find it?

C4 Differentiation

2 questions can someone help me with... working please so I can understand what you have done help appreciated

7. Given that u=(x/2)-(1/8 sin4x)

show that du/dx= sin^2 2x

8. A circular stain grows in such a way that the rate of increase of its radius is inversely proportional to the square of the radius. Given that the area of the stain at t seconds is A cucib centimeteres squared.

show that dA/dT is proportional to 1/(A^0.5)

please help!!!!

Reply 1

Malik

madad69_81

2 questions can someone help me with... working please so I can understand what you have done help appreciated

7. Given that u=(x/2)-(1/8 sin4x)

show that du/dx= sin^2 2x

u=(x/2)-(1/8)(sin4x)
du/dx= ½ - (1/8)(4cos4x)
.......= ½- ½cos4x
.......= ½ - ½(1-2sin²2x)
.......=½ -½ + sin²2x
.......=sin²2x
Q.E.D

Reply 2

dvs

8.
If the radius is r, then dr/dt = k/r^2, where k is some constant. Now A = pi r^2, and:
dA/dt = d(pi r^2)/dt
= 2pi r dr/dt
= 2pi r (k/r^2)
= (2kpi)/r
= (2k (pi)^(3/2))/(sqrt(pi) r)
= K/sqrt(A)

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