Diffrenetiating cos(yz^2)

  • Thread starter JamesGoh
  • Start date
In summary, the formula for differentiating cos(yz^2) is -yz^2sin(yz^2). The chain rule is used to differentiate the inner function, which is yz^2, and the power rule cannot be used for this function. To differentiate cos(yz^2) with respect to y, the product rule is used, resulting in a derivative of -z^2sin(yz^2). A simpler form for the derivative can be obtained by rewriting cos(yz^2) as cos(z^2)y, which results in a derivative of -z^2sin(z^2)y.
  • #1
JamesGoh
143
0
To differentiate [itex]cos(yz^{2})[/itex] with respect to y


can we simply ignore the [itex]z^{2}[/itex] term in the differentiation ?
 
Physics news on Phys.org
  • #2
yup! since it's with respect to y, z is irrelevant.
 
  • #3
Do not "ignore" it, treat it like a constant!
 
  • #4
treat it like a=z^2.. It's a constant when differentiating with respect to y
 

1. What is the formula for differentiating cos(yz^2)?

The formula for differentiating cos(yz^2) is -yz^2sin(yz^2).

2. What is the chain rule used for in differentiating cos(yz^2)?

The chain rule is used to differentiate the inner function, which in this case is yz^2. It allows us to break down the function into smaller, more manageable parts.

3. Can I use the power rule to differentiate cos(yz^2)?

No, the power rule can only be used for functions with a constant as the base. In this case, the base is not a constant but a variable, z.

4. How do I differentiate cos(yz^2) with respect to y?

To differentiate cos(yz^2) with respect to y, we use the product rule. The derivative will be -z^2sin(yz^2).

5. Is there a simpler form for the derivative of cos(yz^2)?

Yes, if we rewrite cos(yz^2) as cos(z^2)y, then the derivative will be -z^2sin(z^2)y.

Similar threads

MHB -x4.6 Find extrema f(x, y, z) = x + yz
    • Calculus
Replies
4
Views
2K
Flux through top part of sphere
    • Calculus and Beyond Homework Help
Replies
6
Views
959
MHB Visualizing a Circle on a 3D Graph Using Parameterization
    • Calculus
Replies
3
Views
1K
I Reasoning behind Infinitesimal multiplication
    • Calculus
Replies
22
Views
2K
B Trigonometric substitution, a case I'd like to share
    • Calculus
Replies
3
Views
1K
MHB Inequality in Triangle: Prove $|x^2+y^2+z^2-2(xy+yz+xz)|\le \frac{1}{27}$
    • General Math
Replies
1
Views
802
I Calculating the change of the volume of a sphere using this integral
    • Calculus
Replies
3
Views
647
I Questions about these Trigonometry Graphs involving sin() and cos()
    • Calculus
Replies
3
Views
1K
MHB Prove $0\le xy+yz+zx-2xyz\le7/27$ for $x+y+z=1$
    • Math POTW for Secondary and High School Students
Replies
1
Views
780
B Question about change of variables
    • Calculus
Replies
29
Views
717

Hot Threads

Recent Insights

Back
Top