Question

question
find $\frac{d}{dx}(sqrt{49x^{-9}})$.
provide your answer below:
$\frac{d}{dx}(sqrt{49x^{-9}})=square$

Explanation:

Step1: Rewrite the function

Rewrite $\sqrt{49x^{-9}}$ as $(49x^{-9})^{\frac{1}{2}}=7x^{-\frac{9}{2}}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^n$, then $\frac{dy}{dx}=anx^{n - 1}$. Here $a = 7$ and $n=-\frac{9}{2}$. So $\frac{d}{dx}(7x^{-\frac{9}{2}})=7\times(-\frac{9}{2})x^{-\frac{9}{2}-1}$.

Step3: Simplify the result

$7\times(-\frac{9}{2})x^{-\frac{9}{2}-1}=-\frac{63}{2}x^{-\frac{11}{2}}$.

Answer:

$-\frac{63}{2}x^{-\frac{11}{2}}$