Question: Could someone help me with this? I need to write down 4 REAL LIFE examples of the following derivative rules: TTHIS IS ONE EXAMPLE SO

Could someone help me with this?

I need to write down 4 REAL LIFE examples of the following derivative rules:

TTHIS IS ONE EXAMPLE SO YOU UNDERSTAND WHAT I NEED

The constant rule says, in Lebesgue's, apostrophy ', notation, that f(x)=c has derivative f'(x)=0.

And here is the example given to this case: f(x)=32 (in physics, the gravity acceleration on earth surface in ft/sq sec) has derivative f(x)=0

(32 is an example of a constant).

Here is what i need 4 examples for:

  1. PRODUCT RULE: the derivative of the product of two functions f(x).g(x) is the derivative of the first times the second, unchanged, plus the first function unchanged, times the derivative of the second.
  2. QUOTIENT RULE: the derivative of the quotient of 2 functions f(x)/g(x) is a quotient with the numerator the same as the result of the product rule, except for minus in place of plus. and the denominator the square of g(x)
  3. the chain rule: the derivative of the composition of 2 functions f(g(x)) is the product of the derivative of the outside functions d/du f(u) with respect to a new variable representing the inside u=g(x), times the derivative of the inside function d/dx g(x)
  4. the chain rule combined with the power rule: when the outside function is a power function, the derivative of f(g(x))=(g(x))A is the product of AuA-1 (which is equal to A(g(x))A-1) times d/dx g(x)

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