1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ehidna [41]
1 year ago
5

Find r'(t), r(t0), and r'(t0) for the given value of (t0). r(t) = (e^t, e²t), t0 = 0​

Mathematics
1 answer:
creativ13 [48]1 year ago
5 0

Applying the differentiation rule, it can be obtained that:

r'(t)=(e^t,2e^{2t}), r(t_0)=(1,1) and r'(t_0)=(1,2).

<h3>What is the formula for differentiating an exponential function?</h3>

The exponential function exists a mathematical function designated by f(x)=\exp or e^{x}. Unless otherwise determined, the term generally directs to the positive-valued function of a real variable, although it can be extended to complex numerals or generalized to other mathematical objects like matrices or Lie algebras.

In mathematics, the derivative of a function of a real variable estimates the sensitivity to change of the function value affecting a change in its statement. Derivatives exist as a fundamental tool of calculus.

\frac{d}{dt}(e^{mt})=me^{mt}.

Given that r(t)=(e^t,e^{2t}).

So, differentiating r(t)=(e^t,e^{2t}) with respect to t, we get: r'(t)=\left(\frac{d}{dt}(e^t),\frac{d}{dt}(e^{2t})\right).

So, using the above formula \frac{d}{dt}(e^{mt})=me^{mt}, we get: r'(t)=(e^t,2e^{2t}).

Now, substituting t=t_0=0 in r(t)=(e^t,e^{2t}) and r'(t)=(e^t,2e^{2t}), we obtain:

r(t_0=0)=(e^0,e^{2\times 0})=(1,1) and r'(t_0=0)=(e^0,2e^{2\times 0})=(1,2).

Therefore, applying the differentiation rule, we get:

r'(t)=(e^t,2e^{2t}), r(t_0)=(1,1) and r'(t_0)=(1,2).

To know about the differentiation rule, refer:

brainly.com/question/25081524

#SPJ9

You might be interested in
PLZ HELP
olasank [31]
Andy money doubled. i.e. $3000
The second day made profit. $3000 + $165
Later he lost $238
The expression is:
2*1500 + $165 -$238

Good luck.
4 0
3 years ago
Read 2 more answers
To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powder with cups of water. Crea
user100 [1]

Answer:

This should help

Step-by-step explanation:

8 0
2 years ago
What is the volume of a box with a length of 3 and 3/4, width of 3, and height of 3 and 1/4?
uysha [10]

Answer:

V= 36 9/16 or (decimal form) 36.5625

Step-by-step explanation:

V=length x width x height

5 0
3 years ago
What is the value of 5 to the power of 4 over 5 to the power of 6?
belka [17]

5^4÷ 5^6=5^-2

1 over 25

8 0
3 years ago
Read 2 more answers
If triangle ABD is similar to Triangle EFG, find BC and FH
Liula [17]

Answer:

B. BC=12, FH=9

Step-by-step explanation:

I guessed and it was right

7 0
3 years ago
Other questions:
  • The diagonal of a cube is 28 cm. Identify the length of an edge. Round to the nearest tenth, if necessary. HELP PLEASE!!
    7·1 answer
  • What is seven minus eight over three?
    12·2 answers
  • Pls help me guys!<br> Thanks =D
    11·1 answer
  • A company is designing a new cylindrical water bottle. The volume of the bottle will be 186 cm the height of the water bottle is
    15·1 answer
  • The shorter tree is 10.5 ft. tall, and casts a shadow that is 11.25 feet long.if the taller tree casts a 17.5 ft. shadow,how tal
    5·1 answer
  • Solve for x
    12·1 answer
  • Factor completely, show work.<br><br> x² - 49
    13·1 answer
  • Someone pls help me with these worksheets :&lt;
    8·1 answer
  • Which lines are parallel? how do you know?
    8·1 answer
  • Evaluate the following expressionsYour answer must be an exact angle in radians and in the interval Example: Enter pi/6 for lcei
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!