Differentiation — Chapter Summary

The derivative of a function f(x)

The derivative of a function f(x) is defined as the limit of the difference quotient as the change in x approaches zero: f'(x) = limₕ→₀ [f(x+h) - f(x)

The derivative dy/dx at a point

The derivative dy/dx at a point on a curve represents the slope of the tangent line to the curve at that point. If the tangent is horizontal, the deri

Also known as the delta method

Also known as the delta method, it involves computing the derivative using the definition: f'(x) = limₕ→₀ [f(x+h) - f(x)] / h. This method is used to

Standard rules include

Standard rules include: Power Rule (d/dx(xⁿ) = nxⁿ⁻¹), Sum/Difference Rule (derivative of sum is sum of derivatives), Product Rule (uv)' = u'v + uv',

The derivative of the first derivative

The derivative of the first derivative is called the second derivative, denoted by d²y/dx² or f''(x). It measures the rate of change of the slope, ind