hw_2.1_basic derivative rules\n9. submit answer practice similar\nattempt 1: 10 attempts remaining.\ndifferen…

hw_2.1_basic derivative rules\n9. submit answer practice similar\nattempt 1: 10 attempts remaining.\ndifferentiate the following function: $y = x^{-\frac{2}{5}}$ $y=$

hw_2.1_basic derivative rules\n9. submit answer practice similar\nattempt 1: 10 attempts remaining.\ndifferentiate the following function: $y = x^{-\frac{2}{5}}$ $y=$

Answer

Explanation:

Step1: Recall power - rule for differentiation

The power - rule states that if $y = x^n$, then $y'=nx^{n - 1}$.

Step2: Identify the value of n

For the function $y=x^{-\frac{2}{5}}$, we have $n =-\frac{2}{5}$.

Step3: Apply the power - rule

$y'=-\frac{2}{5}x^{-\frac{2}{5}-1}=-\frac{2}{5}x^{-\frac{2 + 5}{5}}=-\frac{2}{5}x^{-\frac{7}{5}}$

Answer:

$-\frac{2}{5}x^{-\frac{7}{5}}$