Question
Question: If y = sin<sup>n</sup>x cos nx, then \(\frac{dy}{dx}\)=...
If y = sinnx cos nx, then dxdy=
A
n sinn–1x cos (n – 1)x
B
n sinn–1x cos (n + 1)x
C
n sinn–1 x sin (n – 1)x
D
n sinn–1 x sin (n + 1)x
Answer
n sinn–1x cos (n + 1)x
Explanation
Solution
y = sinnx cos nx
dxdy= – sinnx . n sin nx + cos nx . n sinn–1x cos x
= n sinn–1x (– sin x. sin nx + cos nx cos x)
= n sinn–1x cos(nx + x)