Finding derivatives

 To find the derivative of a function, you can use the rules of differentiation. Here are the basic steps:


1. Power Rule:

   - If you have a term in the form \(ax^n\), where \(a\) is a constant and \(n\) is a real number, the derivative is \(nax^{(n-1)}\).


2. Sum and Difference Rule:

   - If you have a function that is a sum or difference of terms, find the derivative of each term separately.


3. Constant Multiple Rule:

   - If you have a term \(c \cdot f(x)\), where \(c\) is a constant and \(f(x)\) is a function, the derivative is \(c \cdot f'(x)\), where \(f'(x)\) is the derivative of \(f(x)\).


4. Product Rule

   - If you have a product of two functions, say \(u(x) \cdot v(x)\), the derivative is \(u'v + uv'\), where \(u'\) and \(v'\) are the derivatives of \(u\) and \(v\), respectively.


5. Quotient Rule:

   - If you have a quotient of two functions, say \(\frac{u(x)}{v(x)}\), the derivative is \(\frac{u'v - uv'}{(v(x))^2}\).


6. Chain Rule:

   - If you have a composition of functions, such as \(g(f(x))\), the chain rule states that the derivative is \(g'(f(x)) \cdot f'(x)\).


These rules provide a systematic way to find the derivative of a wide range of functions. It's important to practice and become familiar with these rules to efficiently find derivatives in various situations.

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