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