Is z^2 a Constant When Differentiating cos(yz^2) with Respect to y?

  • Thread starter JamesGoh
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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
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To differentiate [itex]cos(yz^{2})[/itex] with respect to y


can we simply ignore the [itex]z^{2}[/itex] term in the differentiation ?
 
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  • #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
 

FAQ: Is z^2 a Constant When Differentiating cos(yz^2) with Respect to y?

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

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

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.

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).

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.

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