How do you use the power rule to differentiate $f(x)=3x^5+2/sqrtx$ ?

Question

1964 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-22T21:07:26

$f'(x)=15x^4-1/x^(3/2)$

We can rewrite the equation so we can apply the power rule.

$f(x)=3x^5+2x^(-1/2)$

Then when we differentiate using the power rule:

$f'(x) = d/dx(3x^5)+d/dx(2x^(-1/2))$

$f'(x) = (3)(5)(x^(5-1))+(2)(-1/2)(x^(-1/2-1))$

How do you use the power rule to differentiate f(x)=3x^5+2/sqrtxf(x)=3x^5+2/sqrtx?