4 √ x − 10/x^6 Find the derivative

Question

Find the derivative

Answer 1

Rewrite as 4x^1/2 - 10x⁶ and use the power rule.

Answer 2

The derivative of x^k ,where k is a real number, is given by k*x^k-1.

The first term of the function you provided can be written as 4x^1/2 while the second term can be written as 10*x^-6 .Thus your function can be re-written as 4x^1/2-10x^-6 .

By applying the rule I reminded above, the derivative of this function is given by

4*(1/2)*x^{1/2 -1} - 10*(-6)x^-6-1=2x^-1/2 +60x^-7

You can leave the result like that or write it as 2/sqrt(x) + 60/x⁷ , where sqrt(x) is the square root of x.

^Best,

^Davide