For two differentiable functions and , the derivative of the composite function is given by: or, equivalently:
If the function is differentiable:
If , where and are constants, then:
If , where is an integer, then:
Derivative of the Logarithmic Function
If , then:
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.