How do you solve this problem? Explain step by step. Thank you.

Find the derivative of  #f(x)=(x/100)^-20#

1 Answer
Sep 20, 2017

#(df)/(dx)=-2xx10^41/x^21#

Explanation:

Recall that derivative of #x^n# is #nx^(n-1)#

hence derivative of #x^(-20)# is #-20x^(-21)=-20/x^21#

As #f(x)=(x/100)^(-20)=1/100^(-20)xx x^(-20)#

Hence #(df)/(dx)=1/100^(-20)xx(-20/x^21)#

= #-20xx100^20/x^21#

= #-2xx10^41/x^21#