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Show work and answer if you can only help.....no spam

Show work and answer if you can only help.....no spam-example-1
User Ytoledano
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We know that h is a vector-valued function. This means it takes one number as an input (t) ,but it outputs two numbers as a two-dimensional vector.

Finding the derivative of a vector-valued function is pretty straightforward. Suppose a vector-valued function is defined as
u(t)=(v(t),w(t)) then its derivative is the vector-valued function
u'(t)=(v'(t),w'(t)) .

In other words, the derivative is found by differentiating each of the expressions in the function's output vector.

Recall that
h(t)=(2t^3+6,e^(2t))

Let's differentiate the first expression:


(d)/(dt) (2t^3+6)=3*2t^2) = 6t^2

Let's differentiate the second expression:


(d)/(dt)(e^2^t)= 2e^2^t

Now let's put everything together:


h′(t) = (d)/(dt)(2t^3+6),(d)/(dt)(e^2^t))


= 6t^2,2e^2^t

In conclusion,
h'(t) = (6t^2,2e^2^t)
User Nasser Abachi
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