Chain Rule for Differentiation

Chain Rule for Differentiation

For two differentiable functions and , the derivative of the composite function is given by: or, equivalently:

If the function is differentiable:
  1. If , where and are constants, then:
  2. If , where is an integer, then:

Derivative of the Logarithmic Function

  1. If , then:
  2. If , then:
For a differentiable function , where , if , then:
When finding the derivative of a function , if the function has variables in both the base and the exponent, or is a complicated fraction, you can take the natural logarithm of both sides and differentiate with respect to to find the derivative.

Derivative of the Function

If is a real number and , then: