Question

Techniques of derivative

Answer 1

[AI-generated answer — Bot]

1. Power Rule: The power rule is the technique to find the derivative of a power of x. If f(x) = xn, then f'(x) = nx^(n-1).

2. Product Rule: The product rule is used when we want to find the derivative of a product of two functions f(x) and g(x). If f(x) and g(x) are differentiable, then (f(x)g(x))' = f'(x)g(x) + f(x)g'(x).

3. Quotient Rule: The quotient rule is used when we want to find the derivative of the quotient of two functions f(x) and g(x). If f(x) and g(x) are differentiable and g(x) is not equal to 0, then [f(x)/g(x)]' = [f'(x)g(x) - f(x)g'(x)]/[g(x)]^2.

4. Chain Rule: The chain rule is used when we want to find the derivative of a composite function f(g(x)). If f(x) and g(x) are differentiable, then f'(g(x))g'(x).

5. Exponential Rule: The exponential rule is used when we want to find the derivative of a function of the form f(x) = e^(g(x)). The derivative of f(x) is f'(x) = g'(x)e^(g(x)).

6. Logarithmic Rule: The logarithmic rule is used when we want to find the derivative of a function of the form f(x) = ln(g(x)). The derivative of f(x) is f'(x) = g'(x)/g(x).

7. Implicit Differentiation: Implicit differentiation is used when we want to find the derivative of a function where the formula does not explicitly related y to x. In such cases, one can differentiate with respect to x on both sides of the equation and solve for y'.