f(t)=sin(2t)-t cos(t)  

Answered question

2022-01-14

f(t)=sin(2t)-t cos(t)

Answer & Explanation

Vasquez

Vasquez

Expert2022-02-06Added 669 answers

 

Find the derivative of the following via implicit differentiation:
ddt(f(t))=ddt(tcos(t)+sin(2t))

Using the chain rule, ddt(f(t))=df(u)dududt, where u=t and ddu(f(u))=f(u):
(ddt(t))f(t)=ddt(tcos(t)+sin(2t))

The derivative of t is 1:
1f(t)=ddt(tcos(t)+sin(2t))

Differentiate the sum term by term and factor out constants:
f(t)=((ddt(tcos(t)))+ddt(sin(2t)))

Use the product rule, ddt(uv)=vdudt+udvdt, where u=t and v=cos(t):
f(t)=ddt(sin(2t))(cos(t)(ddt(t))+t(ddt(cos(t))))

Simplify the expression:
f(t)=cos(t)(ddt(t))t(ddt(cos(t)))+ddt(sin(2t))

The derivative of t is 1:

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