1. MIRDA PRISMA WIJAYANTO
PHYSICS INTERNATIONAL EDUCATIONPROGRAM
NIM 120210152032
“ BASIC MATHEMATICS ASSIGNMENT “
We have a function F(x) = ( x – 3 )7 tan2 ( sin3 (2x-3)5 ), find :
a. F’(x)
b. F”(x)
c. Find the formula of tangent line at point (
3
2
, −
2187
128
)
d. Find the maximum and minimum local, maximum and minimum absolute, and the
inflection point on interval ( -π, π )
ANSWER :
BASIC FORMULAS :
1. sin3
x = sinx.sinx.sinx
sin3
x’
= a. U’
V + V’
U
cosx.sinx + cosx.sinx = 2.sinx.cosx
b. U’
V + V’
U
cosx.sin2
x +2.sinx.cosx.sinx = 3. sin2
x.cosx
sin3
x’
= 3. sin2
x.cosx
2. tan2
x = tanx.tanx
tan2
x’
= U’
V + V’
U
= sec2
x.tanx+ sec2
x.tanx = 2.sec2
x.tanx
tan2
x’
= 2.sec2
x.tanx
3. sec2
x = secx.secx
sec2
x’
= U’
V + V’
U
= (secx.tanx)secx+(secx.tanx)secx = 2.sec2
x.tanx
sec2
x’
= 2.sec2
x.tanx
1. Finding F’
(x) = [( x – 3 )7
tan2
( sin3
(2x-3)5
)]’
a.) Derivation of ( sin3
(2x-3)5
)