But this does not account for the x in the numerator of the integrand. Use substitution to find the antiderivative of x x 1 dx. For example sin 2 (4x) is a composite of three functions u 2, usin(v) and v4x. By breaking down the function into its components, sqrt(x) and 3x2-x, we demonstrate how their derivatives work together to make differentiation easier. In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives of f and g. Example 5.5.4: Finding an Antiderivative Using u -Substitution. An example that combines the chain rule and the quotient rule: (The fact that this may be simplified to is more or less a happy coincidence unrelated to the chain rule.) The chain rule can be extended to composites of more than two functions. Lets dive into the process of differentiating a composite function, specifically f(x)sqrt(3x2-x), using the chain rule.
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