- #1
Mary4ever
- 11
- 0
Homework Statement
Differentiate:
Homework Equations
y=∛((7-3x^2)^2)
The Attempt at a Solution
y^'(x)=(4x(3x^2-7))/(∛((7-3x^2 )^2))^2 )
How to Differentiate a Cubic Root Function with a Square Expression Inside?
- Thread starter Mary4ever
- Start date
-
- Tags
- Differentiate Function
In summary: This was the advice I gave in post #2. It's much more convenient to write your function as y = (7 - 3x2)2/3. When you're differentiating, it's almost always better to rewrite expressions with radicals using exponents. Your answer might be correct, but if so, it needs to be simplified.If you differentiated the function that I wrote, you would get: y'(x)=12x^3-28x
Differentiate:
y=∛((7-3x^2)^2)
y^'(x)=(4x(3x^2-7))/(∛((7-3x^2 )^2))^2 )
- #2
Mark44
Mentor
- 37,784
- 10,175
Mary4ever said:
It's much more convenient to write your function as y = (7 - 3x2)2/3. When you're differentiating, it's almost always better to rewrite expressions with radicals using exponents. Your answer might be correct, but if so, it needs to be simplified.
- #3
Mary4ever
- 11
- 0
I really need to know if it is correct, could you please let me know if it is?
- #4
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
(try using the X2 button just above the Reply box 
)
that looks correct, but it needs simplifying
(also, it's a ridiculous way of writing it, and you'll lose marks in the exam if you do that)
)Mary4ever said:
that looks correct, but it needs simplifying
(also, it's a ridiculous way of writing it, and you'll lose marks in the exam if you do that)
- #5
Mary4ever
- 11
- 0
Thank you for you reply. So what would be the correct way to write it so I do not lose marks for it?
- #6
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
first, simplify it, as Mark44 suggested
suggested- #7
Mary4ever
- 11
- 0
Is this correct: y = (((7-3x^2)^2))^ (1/3)
dy/dx = (1/3) (((7-3x^2)^2))^ (-2/3) (2(7-3x^2)(-6x))
= (24/9)(7x - 3x^3) / ∛((7-3x^2)^4)
dy/dx = (1/3) (((7-3x^2)^2))^ (-2/3) (2(7-3x^2)(-6x))
= (24/9)(7x - 3x^3) / ∛((7-3x^2)^4)
- #8
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
Mary4ever said:
i'm sorry, but can't you see how ridiculous that is?
why not just write y = (7-3x2)2/3 ?
- #9
Mary4ever
- 11
- 0
ok so is this a correct final answer now: y'(x)=4x(3x^2-7) ??
- #10
cmcraes
- 99
- 6
The solution is
12x(3x^(2)-7) isn't it?
12x(3x^(2)-7) isn't it?
- #11
cmcraes
- 99
- 6
Sorry never mind thought you said derivative not differentiate!
- #12
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
Mary4ever said:
how did you get that?
- #13
Mark44
Mentor
- 37,784
- 10,175
No.cmcraes said:
You get the derivative when you differentiate a function. It seems that you didn't know this.cmcraes said:
- #14
Mary4ever
- 11
- 0
I am really confused now, what is the correct answer then?
- #15
Mark44
Mentor
- 37,784
- 10,175
Mary4ever said:
This was the advice I gave in post #2.
What do you get if you differentiate the function that I wrote? You need to use the chain rule (correctly).Mark44 said:
- #16
Mary4ever
- 11
- 0
Differentiating the function you wrote would get: y'(x)=12x^3-28x
Is this correct? Please help
Is this correct? Please help
- #17
tiny-tim
Science Advisor
Homework Helper
- 25,839
- 258
no
show us, step-by-step, how you got that
show us, step-by-step, how you got that
FAQ: How to Differentiate a Cubic Root Function with a Square Expression Inside?
What does it mean to differentiate a function?
Differentiating a function means finding its derivative, which represents the rate of change of the function at any given point. It tells us how much the output of the function changes with respect to its input.
Why do we differentiate functions?
We differentiate functions to solve problems involving rates of change, such as finding the maximum or minimum value of a function, determining the slope of a tangent line, or analyzing the behavior of a system over time.
What is the process for differentiating a function?
The process of differentiating a function involves using specific rules and formulas, such as the power rule, product rule, quotient rule, and chain rule, to find the derivative of the function. It requires understanding the basic properties of functions and how they behave when we manipulate them algebraically.
What are some real-life applications of differentiating functions?
Differentiating functions has many practical applications in fields such as physics, engineering, economics, and statistics. For example, in physics, we use differentiation to determine the velocity and acceleration of an object, while in economics, we use it to analyze the marginal cost and revenue of a business.
What is the relationship between differentiating a function and integrating a function?
Differentiating and integrating are inverse operations. This means that the process of finding the derivative of a function is the opposite of finding the integral of the function. In other words, differentiation "undoes" integration and vice versa. They are both important concepts in calculus and are used to solve a variety of problems in mathematics and science.