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
givi [52]
3 years ago
10

3√x -2/x^2please show step by step of differentiation before combining the terms. ​

Mathematics
1 answer:
EastWind [94]3 years ago
3 0

Answer:

Step-by-step explanation:

Before we differentiate, let us assign a variable to the function. Let y be equal to the function i.e let y = 3√x -2/x²

In differentiation if y = ax^{n}, then \frac{dy}{dx} = nax^{n-1} where n is a constant and dy/dx means we are differentiating the function y with respect to x.

Applying the formula o the question given;

y= 3\sqrt{x}  -2/x^2\\y = 3{x}^\frac{1}{2}  - 2x^{-2} \\\\

On differentiating the resulting function;

\frac{dy}{dx} = \frac{1}{2}*3x^{\frac{1}{2}-1 }   - (-2)x^{-2-1} \\\\\frac{dy}{dx} = \frac{1}{2}*3x^{-\frac{1}{2}} + 2x^{-3}\\ \\\frac{dy}{dx} = \frac{1}{2}*{\frac{3}{x^{\frac{1}{2} } }} + \frac{2}{x^{3} } \\\\\frac{dy}{dx} = {\frac{3}{2x^{\frac{1}{2} } }} + \frac{2}{x^{3} }\\\\\frac{dy}{dx} = {\frac{3}{2\sqrt{x}  }} + \frac{2}{x^{3} }

To combine the terms, we will add up by finding their LCM.

\frac{dy}{dx} = {\frac{3}{2\sqrt{x}  }} + \frac{2}{x^{3} }\\\frac{dy}{dx}  = \frac{3x^3+4\sqrt{x} }{2x^{3} \sqrt{x}}

You might be interested in
What is 662/3% as a fraction simplest form
Mrac [35]

Answer:

331/150

Step-by-step explanation:

662/3% = (662/3)/100=662/300=331/150

4 0
3 years ago
Hello! Please help. <br> "Find the error &amp; explain why it is wrong."
mixas84 [53]

Answer: Step E

Step-by-step explanation:

The error is in the last step. In Step D, we see that we're supposed to subtract the second part from the first part. We also see we have the terms 2x-8 in the numerator on the right. Since we're subtracting, the expression should actually be -2x +8. 3 -2x +8 should be -2x +11 which is not the numerator in Step E so the last step is wrong.

5 0
3 years ago
Please help the problem is in the picture provided below.
Nadya [2.5K]

Answer:

sorry I don't know

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
A sweater for 36.00 at 7% sales tax
blagie [28]
$36 x 1.07 = $38.52
The cost will be $38.52
Tax on this is $2.52
4 0
3 years ago
8=56<br> 7=42<br> 6=30<br> 5=20<br> 3=?
m_a_m_a [10]
3=6

In this case, the pattern is the number, in this case, 3, multiplied by the number below it.

See?
8\times7=56\\7\times6=42\\6\times5=30\\5\times4=20\\3\times2=6

Hope this helped :)
3 0
2 years ago
Read 2 more answers
Other questions:
  • One year Hank had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher
    9·1 answer
  • If the eccentricity of an ellipse is 0.43 and the length of its major axis is 11 units, how far from the center are the foci loc
    14·2 answers
  • Convert 246 tablespoons to teaspoons [1tbsp=3tsp]
    12·2 answers
  • Sherry bought a dozen daisies are $8.76 how much does a single daisy cost
    7·2 answers
  • Log(5) + log(3) rewrite the following in the form log(c).
    5·2 answers
  • 7th grade math help me please..
    15·1 answer
  • Can someone please Helppp
    6·1 answer
  • The 100th term of 9​, 93​, 95​, 97​, ...
    6·1 answer
  • Would mind give me only answer​
    6·1 answer
  • (20 POINTS!!!!) Terry realized that 25% of his money was $12.50. He made a double number line to represent this. What number wou
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!