What is the derivative of #4/sqrtx#?

Question

1332 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-02T00:51:49

Following an exponential rule that states #a^(m/n)=root(n)(a^m)#, we can rewrite the fucntion as

#4/x^(1/2)#

Another exponential rule states that #1/a^n=a^-n#

Thus,

#4/x^(1/2)=4x^-(1/2)#

#(dy)/(dx)=(-1/2)4x^(-3/2)=-2x^(-3/2)#

Or, if you prefer the original form, we can go back to the fraction and root:

#(dy)/(dx)=-2/sqrt(x^3)#