quick questions on basic differentiation of the trig functions (1 Viewer)

[Ellie999]

help im stuck.. i'll give you a prize if you can give me explanations and solutions to these Q's below...
Differentiate the following with respect to x:
1. Sin^3x
2.Cos^2 2x
thanks v.v. much in advance

 

[webby234]

Use the chain rule:

[f(x)]ⁿ = n[f(x)]^n-1*[f'(x)]
This means; multiply by the power, reduce the power by 1, then multiply by the derivative of the function.

1. sin³x = (sinx)³
d/dx = 3sin²xcosx

2. cos²2x = (cos(2x))²
d/dx = 2(cos2x)¹*-2sin2x
= -4sin(2x)cos(2x)

 

[Ellie999]

ohh i get it now!!!! thanks webby!