We need to find:
z'(t)=dz(t)dt=ddt(e-3t·(-sin(2t))2)=
z'(t)=dz(t)dt=ddt(e-3t·(-sin?(2t))2)=
ddt(e-3tsin2(2t))=e-3tsin(2t)(4cos(2t)-3sin(2t))
ddt(e-3tsin2?(2t))=e-3tsin?(2t)(4cos?(2t)-3sin?(2t))
Using:
The product rule:
ddt(f(t)·y(t))=f(t)·ddt(y(t))+y(t)·ddt(f(t))=y(t)·f'(t)+f(t)·y'(t)
ddt(f(t)·y(t))=f(t)·ddt(y(t))+y(t)·ddt(f(t))=y(t)·f'(t)+f(t)·y'(t)
ddt(ex(t))=ex(t)·ddt(x(t))=x'(t)·ex(t)
ddt(ex(t))=ex(t)·ddt(x(t))=x'(t)·ex(t)
When CC is a constant:
ddt(C·q(t))=C·ddt(q(t))=C·q'(t)
ddt(C·q(t))=C·ddt(q(t))=C·q'(t)
When nn is a constant, using the chain rule:
ddt(w(t)n)=n·w(t)n-1·ddt(w(t))=n·w(t)n-1·w'(t)
ddt(w(t)n)=n·w(t)n-1·ddt(w(t))=n·w(t)n-1·w'(t)
When mm is a constant, using the chain rule:
ddt(v(mt))=ddt(mt)·v'(mt)=m·v'(mt)
