How do you find the derivative of #x(t)=5sint+3cost#?

Answer 1

#x'(t)=5cost-3sint#

Using the #color(blue)"standard derivatives for these terms"#
#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(sinx)=cosx , d/dx(cosx)=-sinx)color(white)(2/2)|)))#
#x(t)=5sint+3cost#
#rArrx'(t)=5cost-3sint#
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Answer 2

To find the derivative of ( x(t) = 5\sin(t) + 3\cos(t) ), you can differentiate each term separately using the chain rule. The derivative of ( \sin(t) ) is ( \cos(t) ), and the derivative of ( \cos(t) ) is ( -\sin(t) ). Therefore, the derivative of ( 5\sin(t) ) is ( 5\cos(t) ), and the derivative of ( 3\cos(t) ) is ( -3\sin(t) ). Combining these results, the derivative of ( x(t) ) with respect to ( t ) is ( x'(t) = 5\cos(t) - 3\sin(t) ).

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Answer 3

To find the derivative of ( x(t) = 5 \sin(t) + 3 \cos(t) ), we will use the derivative rules for trigonometric functions.

The derivative of ( \sin(t) ) is ( \cos(t) ) and the derivative of ( \cos(t) ) is ( -\sin(t) ). Using these derivative rules, we can find the derivative of ( x(t) ) term by term.

( \frac{d}{dt}[5\sin(t)] = 5\cos(t) )

( \frac{d}{dt}[3\cos(t)] = -3\sin(t) )

Therefore, the derivative of ( x(t) ) with respect to ( t ) is:

( \frac{dx}{dt} = 5\cos(t) - 3\sin(t) )

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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.

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.

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.

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.

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