First Derivative of (5/x)+(5/SQRT(x)): Homework Equations & Rules to Solve

  • Thread starter Thread starter Government$
  • Start date Start date
  • Tags Tags
    Derivative
Click For Summary
SUMMARY

The first derivative of the function (5/x) + (5/SQRT(x)) is calculated using the power rule rather than the quotient rule. The derivative is expressed as d/dx(5x-1 + 5x-1/2) which simplifies to -5x-2 - (1/2)x-3/2. This approach streamlines the differentiation process and confirms the correctness of the solution provided.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically derivatives.
  • Familiarity with the power rule for differentiation.
  • Knowledge of the notation for derivatives (d/dx).
  • Ability to manipulate algebraic expressions involving exponents.
NEXT STEPS
  • Study the power rule in greater detail to solidify understanding.
  • Learn about the quotient rule for differentiation and when to apply it.
  • Practice additional derivative problems involving rational and radical functions.
  • Explore applications of derivatives in real-world scenarios, such as optimization problems.
USEFUL FOR

Students studying calculus, particularly those focusing on differentiation techniques, as well as educators looking for clear examples of applying the power rule in derivative calculations.

Government$
Messages
87
Reaction score
1

Homework Statement


Find the first derivative of (5/x)+(5/SQRT(x))


Homework Equations



Derivative ruls

The Attempt at a Solution


attachment.php?attachmentid=53629&stc=1&d=1354648651.jpg


Is this correct? Thank you
 

Attachments

  • IMG_0289.JPG
    IMG_0289.JPG
    16 KB · Views: 444
Physics news on Phys.org
Yes.
 
Thank you
 
Unless this problem requires the use of the quotient rule, it can be done much more simply using the power rule.

$$\frac{d}{dx}\left(\frac{5}{x} + \frac{5}{\sqrt{x}} \right)$$
= d/dx(5x-1 + 5x-1/2)
= -5x-2 - (1/2)x-3/2
 

Similar threads

Multivariable calculus problem involving partial derivatives along a surface
  • · Replies 9 ·
Replies
9
Views
2K
Integration with Respect to x: Integral of sqrt((5-x)/x)
  • · Replies 18 ·
Replies
18
Views
4K
Derivative of -x using first principle
  • · Replies 5 ·
Replies
5
Views
2K
Finding the Derivative of y=sqrt(x+sqrt(x+sqrt(x)))
  • · Replies 7 ·
Replies
7
Views
3K
How Can I Solve This Differential Equation for x(y)?
  • · Replies 7 ·
Replies
7
Views
1K
Constructing cubic spline interpolation polynomials
  • · Replies 4 ·
Replies
4
Views
1K
Find Directional Derivative at Given Point in Direction of Given Vector
  • · Replies 7 ·
Replies
7
Views
2K
Why Is the Chain Rule Not Used in Differentiating h(x) = 3f(x) + 8g(x)?
  • · Replies 2 ·
Replies
2
Views
2K
Trying To Use Squeeze Theorem To Prove Derivatives Are Equal
  • · Replies 4 ·
Replies
4
Views
2K
Find Coordinates of Closest Point on y=sqrt(x) to (4,0)
  • · Replies 3 ·
Replies
3
Views
1K