MAT2691
ASSIGNMENT 1
2023
, Solution:
1.1).
𝑦 = sinh−1 (cos2 (x))
du
𝐿𝑒𝑡: 𝑢 = cos2 (x) ⇒ = −2 cos(x) sin(x)
dx
𝑦 = sinh−1(u)
dy 1 1 1
= = =
du √u2 + 1 2 √cos4 (x) + 1
√(cos2 (x)) + 1
𝑈𝑠𝑖𝑛𝑔 𝐶ℎ𝑎𝑖𝑛 𝑅𝑢𝑙𝑒:
dy dy du
= ×
dx du dx
dy 1
= (−2 cos(x) sin(x))
dx √cos4 (x) + 1
dy 2 cos(x) sin(x)
=−
dx √cos 4 (x) + 1
dy 2 sin(2x)
=−
dx √cos 4 (x) + 1
ASSIGNMENT 1
2023
, Solution:
1.1).
𝑦 = sinh−1 (cos2 (x))
du
𝐿𝑒𝑡: 𝑢 = cos2 (x) ⇒ = −2 cos(x) sin(x)
dx
𝑦 = sinh−1(u)
dy 1 1 1
= = =
du √u2 + 1 2 √cos4 (x) + 1
√(cos2 (x)) + 1
𝑈𝑠𝑖𝑛𝑔 𝐶ℎ𝑎𝑖𝑛 𝑅𝑢𝑙𝑒:
dy dy du
= ×
dx du dx
dy 1
= (−2 cos(x) sin(x))
dx √cos4 (x) + 1
dy 2 cos(x) sin(x)
=−
dx √cos 4 (x) + 1
dy 2 sin(2x)
=−
dx √cos 4 (x) + 1
