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
alexdok [17]
3 years ago
6

Find the differential coefficient of

{2x}(1+Lnx)" alt="e^{2x}(1+Lnx)" align="absmiddle" class="latex-formula">​
Mathematics
1 answer:
Gemiola [76]3 years ago
6 0

Answer:

\rm \displaystyle y' =   2 {e}^{2x}   +    \frac{1}{x}  {e}^{2x}  + 2 \ln(x) {e}^{2x}

Step-by-step explanation:

we would like to figure out the differential coefficient of e^{2x}(1+\ln(x))

remember that,

the differential coefficient of a function y is what is now called its derivative y', therefore let,

\displaystyle y =  {e}^{2x}  \cdot (1 +   \ln(x) )

to do so distribute:

\displaystyle y =  {e}^{2x}  +   \ln(x)  \cdot  {e}^{2x}

take derivative in both sides which yields:

\displaystyle y' =  \frac{d}{dx} ( {e}^{2x}  +   \ln(x)  \cdot  {e}^{2x} )

by sum derivation rule we acquire:

\rm \displaystyle y' =  \frac{d}{dx}  {e}^{2x}  +  \frac{d}{dx}   \ln(x)  \cdot  {e}^{2x}

Part-A: differentiating $e^{2x}$

\displaystyle \frac{d}{dx}  {e}^{2x}

the rule of composite function derivation is given by:

\rm\displaystyle  \frac{d}{dx} f(g(x)) =  \frac{d}{dg} f(g(x)) \times  \frac{d}{dx} g(x)

so let g(x) [2x] be u and transform it:

\displaystyle \frac{d}{du}  {e}^{u}  \cdot \frac{d}{dx} 2x

differentiate:

\displaystyle   {e}^{u}  \cdot 2

substitute back:

\displaystyle    \boxed{2{e}^{2x}  }

Part-B: differentiating ln(x)•e^2x

Product rule of differentiating is given by:

\displaystyle  \frac{d}{dx} f(x) \cdot g(x) = f'(x)g(x) + f(x)g'(x)

let

  • f(x) \implies   \ln(x)
  • g(x) \implies    {e}^{2x}

substitute

\rm\displaystyle  \frac{d}{dx}  \ln(x)  \cdot  {e}^{2x}  =  \frac{d}{dx}( \ln(x) ) {e}^{2x}  +  \ln(x) \frac{d}{dx}  {e}^{2x}

differentiate:

\rm\displaystyle  \frac{d}{dx}  \ln(x)  \cdot  {e}^{2x}  =   \boxed{\frac{1}{x} {e}^{2x}  +  2\ln(x)  {e}^{2x} }

Final part:

substitute what we got:

\rm \displaystyle y' =   \boxed{2 {e}^{2x}   +    \frac{1}{x}  {e}^{2x}  + 2 \ln(x) {e}^{2x} }

and we're done!

You might be interested in
Help please this is do soon I will mark brainliest
Fed [463]

Answer:

(-3,2)

Step-by-step explanation:

when reflecting over the y axis all you have to do is flip the signs on the x values so it would be (-3,2)

4 0
2 years ago
Estimate 2,141 x 8 i need it now
irakobra [83]
17128.........................
6 0
3 years ago
Find the area of the shaded region in each of the following figure all unit are in cm
vodomira [7]
1st problem:
A = 630 cm


2nd problem:
A = 104 cm

All I can see on the picture you provided.
7 0
3 years ago
What term best describes the graph of y=-2
sesenic [268]

Answer:

It would be constant.

Step-by-step explanation:

Since there is no x value, the line will have no slope and just be horizontal about y= -2.

6 0
2 years ago
How many sq. ft. are in an acre?
Ainat [17]
43560 sq. ft
Answer till 20 characters 
8 0
3 years ago
Read 2 more answers
Other questions:
  • According to government data, the probability that a woman between the ages of 25 and 29 was never married is 40%. in a random s
    11·2 answers
  • The opening in a rectangular door frame measures 9 feet by 3 feet. Each of the four doors described in the table measures
    7·2 answers
  • Solve the differential equation:<br>dy/dx = x/((y^2)sqrt(1+x))
    9·1 answer
  • johnathan class has 30 boys of the students in his class 60% are girls how many girls are in johnathans class
    12·1 answer
  • $29.99 markdown 33 and one third
    10·1 answer
  • 100 more than 146 is
    15·2 answers
  • Phone, it can expect to sell 1,000-2x phones.
    5·1 answer
  • Three triangles are drawn on the same piece of paper such that no two sides are on the same line. What is the maximum number of
    7·1 answer
  • Will give points 1.. Which of the towers did you select? Draw a sketch of your tower. The height you are given is the vertical d
    9·1 answer
  • A teacher gave her class two quizzes. 25% of the class passed both quizzes and 40% of the class passed the first quiz. What perc
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!