Question

derivatives of basic functions: problem 2 (1 point) results for this submission 2 of the answers are not correct. suppose that $f(x)=1x^{3/5}-2x^{2/7}$. evaluate each of the following: $f(2)=$ $f(4)=$ note: you can earn partial credit on this problem. preview my answers submit answers your score was recorded. your score was successfully sent to canvas. you have attempted this problem 2 times. you received a score of 0% for this attempt. your overall recorded score is 0%. you have unlimited attempts remaining.

Explanation:

Step1: Apply power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y'=anx^{n - 1}$. For $f(x)=x^{3/5}-2x^{2/7}$, the derivative $f'(x)$ is $f'(x)=\frac{3}{5}x^{\frac{3}{5}-1}-2\times\frac{2}{7}x^{\frac{2}{7}-1}=\frac{3}{5}x^{-\frac{2}{5}}-\frac{4}{7}x^{-\frac{5}{7}}$.

Step2: Evaluate $f'(2)$

Substitute $x = 2$ into $f'(x)$:

$$
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$$

$$
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$$

$$
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$$

Step3: Evaluate $f'(4)$

Substitute $x = 4$ into $f'(x)$:

$$
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$$

$$
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$$

$$
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$$

Answer:

$f'(2)\approx0.128$, $f'(4)\approx0.129$