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What is the chain rule, product rule and quotient rule and when do I use them?

The chain rule, product rule and quotient rule are all 3 methods of differentiating complex functions.

Chain rule

The chain rule is as follows: (dy/dx) = (dy/dz).(dz/dx) or D{f(g(x))}/dx = f'(g(x)).g'(x)

The chain rule is used when you want to differentiate a function to the power of a number. For example, you would use it to differentiate (4x^3 + 3x)^5

The chain rule is also used when you want to differentiate a function inside of another function. For example, you would use it to differentiate sin(3x) (With the function 3x being inside the sin() function)

Product rule

The product rule is as follows d(f(x).g(x))/dx = g(x).f'(x) + f(x).g'(x)

The product rule is used when you want to differentiate two different functions multiplied together. For example, you would use it to differentiate (x^4 + 7x + 2)(3x^2 + 1)

Quotient rule

The Quotient rule is as follows: d(f(x) / g(x))/dx = (f'(x)g(x) - g(x)f'(x)) / g(x)^2

The Quotient rule is used when you want to differentiate one function divided by another. For example, you would use it to differentiate (4x + 5)/(3 - x^2)

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