Question

Find dy/dx of Y=1/x√x using product rule

Answer 1

Answer:

Step-by-step explanation:

solution  

y = $\frac{1}{x\sqrt{x} }$

in terms of product

⇒ $\frac{1}{x\sqrt{x} }$ = $(x\sqrt{x}) ^{-1}$

∴ $(x\sqrt{x} )^{-1}$ = $x^{-1}$ x $x^{-1/2}$

⇒ dy/dx = $x^{-1}$ x $(-1/2)x^{-3/2}$ + $x^{-1/2}$ x $-x^{-2}$

⇒ dy/dx = (-1/2)$x^{-5/2}$ - $x^{-5/2}$

⇒ dy/dx = $-\frac{3}{2} x^{-5/2}$

⇒ dy/dx = $-\frac{3}{2x^{5/2} }$