What is the derivative of $y'$ given $y = xsqrt(x) + 1/(x^2 sqrt(x))$ ?

Question

1860 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-12T02:06:49

$y'' = 1/4(3x^(-1/2) +35 x^(-9/2))$

$y = xsqrt(x) + 1/(x^2 sqrt(x))$

We are asked to find the derivative of $y'$ which is the second derivative of $y$ , represented by $(d^2y)/dx^2$ or $y''$

First rewrite the expression for $y$ in term of powers of x $->$

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

Using the power rule $->$

$y' = 3/2x^(1/2) - 5/2 x^(-7/2)$

Using the power rule again $->$

$y'' = 3/2 * 1/2 x^(-1/2) - 5/2 * (-7/2) x^(-9/2)$

$y'' = 3/4 x^(-1/2) + 35/4 x^(-9/2)$

$y'' = 1/4(3x^(-1/2) +35 x^(-9/2))$

What is the derivative of y'y' given y = xsqrt(x) + 1/(x^2 sqrt(x))y = xsqrt(x) + 1/(x^2 sqrt(x)) ?