hw10 differentiation rules 1 (targets c1, c5; §3.3)\nscore: 5/9 answered: 6/9\n× question 6\nscore on last…

hw10 differentiation rules 1 (targets c1, c5; §3.3)\nscore: 5/9 answered: 6/9\n× question 6\nscore on last try: 0 of 1 pts. see details for more.\n> next question get a similar question you can retry this question below\nfind the derivative of (f(x)=3sqrt{x}-\frac{2}{x^{7}}).\n(f(x)=\frac{3}{2sqrt{x}}+\frac{4}{x^{3}}) ×\nquestion help: video 1 video 2 message instructor\nsubmit question

hw10 differentiation rules 1 (targets c1, c5; §3.3)\nscore: 5/9 answered: 6/9\n× question 6\nscore on last try: 0 of 1 pts. see details for more.\n> next question get a similar question you can retry this question below\nfind the derivative of (f(x)=3sqrt{x}-\frac{2}{x^{7}}).\n(f(x)=\frac{3}{2sqrt{x}}+\frac{4}{x^{3}}) ×\nquestion help: video 1 video 2 message instructor\nsubmit question

Answer

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=3\sqrt{x}-\frac{2}{x^{7}}$ as $f(x)=3x^{\frac{1}{2}} - 2x^{-7}$.

Step2: Apply power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. For the first term $3x^{\frac{1}{2}}$, its derivative is $3\times\frac{1}{2}x^{\frac{1}{2}-1}=\frac{3}{2}x^{-\frac{1}{2}}=\frac{3}{2\sqrt{x}}$. For the second term $-2x^{-7}$, its derivative is $-2\times(-7)x^{-7 - 1}=14x^{-8}=\frac{14}{x^{8}}$.

Answer:

$f^\prime(x)=\frac{3}{2\sqrt{x}}+\frac{14}{x^{8}}$