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

Answer 1

Luke Alvarez

#f'(t)=((t sin t )', (t^2)', (-t cos t )')=(sint+t cos t, 2t, -cost+t sin t)#

Use product rule.

Also, #(t^n)'=nt^(n-1), (sin t)'=cos t and (cos t)'=-sin t#.

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Answer 2

Paisley Johnson

The derivative of ( f(t) = (t \sin(t), t^2 - t \cos(t)) ) with respect to ( t ) is given by ( f'(t) = (\frac{d}{dt}(t \sin(t)), \frac{d}{dt}(t^2 - t \cos(t))) ). You can find the derivatives of each component function separately using the product rule and chain rule as necessary.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.