find y if y = -6 / √x. y = □
find y if y = -6 / √x. y = □
Answer
Explanation:
Step1: Rewrite the function
Rewrite $y = \frac{-6}{\sqrt{x}}$ as $y=-6x^{-\frac{1}{2}}$.
Step2: Apply the power - rule for differentiation
The power - rule states that if $y = ax^n$, then $y'=anx^{n - 1}$. Here, $a=-6$ and $n =-\frac{1}{2}$. So, $y'=-6\times(-\frac{1}{2})x^{-\frac{1}{2}-1}$.
Step3: Simplify the expression
$y' = 3x^{-\frac{3}{2}}=\frac{3}{x^{\frac{3}{2}}}=\frac{3}{x\sqrt{x}}$.
Answer:
$\frac{3}{x\sqrt{x}}$