# What is the derivative of #f(t) = (tsint , t^2-t tant ) #?

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To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ),The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

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[ f'(t) = \leftTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component withThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left(To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect toThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to (The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sinTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( tThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t +To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t \The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t )The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cosTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos tTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

\The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t,To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \fracThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2tTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{dThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t -To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt}The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan tTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin tThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - tTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t)The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - t \To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t) = \The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - t \secTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t) = \sinThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - t \sec^2To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t) = \sin tThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - t \sec^2 tTo find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t) = \sin t + tThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - t \sec^2 t \To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t) = \sin t + t \The derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - t \sec^2 t \right)To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t) = \sin t + t \cosThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - t \sec^2 t \right) \To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t) = \sin t + t \cos tThe derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ) is:

[ f'(t) = \left( \sin t + t \cos t, 2t - \tan t - t \sec^2 t \right) ]To find the derivative of ( f(t) = (t \sin t, t^2 - t \tan t) ), we differentiate each component with respect to ( t ) separately:

[ \frac{d}{dt} (t \sin t) = \sin t + t \cos t ]

[ \frac{d}{dt} (t^2 - t \tan t) = 2t - (\tan t + t \sec^2 t) ]

So, the derivative of ( f(t) ) is:

[ f'(t) = \left( \sin t + t \cos t, , 2t - \tan t - t \sec^2 t \right) ]

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