What is the derivative of #f(t)=cos^2(3t+5)#?

1 Answer

Answer:

#f'(t)=-6*sin(3t+5)*cos(3t+5)#

Explanation:

#cos^2(3t+5)#
#=cos(3t+5)*cos(3t+5)#

Use product rule:
#=d/dxcos(3t+5)*cos(3t+5)+d/dxcos(3t+5)*cos(3t+5)#

Use the chain rule to differentiate #cos(3t+5)#
#=-sin(3t+5)*3*cos(3t+5)-sin(3t+5)*3*cos(3t+5)#
#=-3*sin(3t+5)*cos(3t+5)-3*sin(3t+5)*cos(3t+5)#

Simplify
#=-6*sin(3t+5)cos(3t+5)#