Apply the quotient rule, which is:
dxdg(x)f(x)=g2(x)−f(x)dxdg(x)+g(x)dxdf(x)
f(x)=1 and g(x)=cos2(x).
To find dxdf(x):
-
The derivative of the constant 1 is zero.
To find dxdg(x):
-
Let u=cos(x).
-
Apply the power rule: u2 goes to 2u
-
Then, apply the chain rule. Multiply by dxdcos(x):
-
The derivative of cosine is negative sine:
dxdcos(x)=−sin(x)
The result of the chain rule is:
−2sin(x)cos(x)
Now plug in to the quotient rule:
cos3(x)2sin(x)