Question

hw10 differentiation rules 1 (targets c1, c5; §3.3) score: 5/9 answered: 5/9 question 6 find the derivative of (f(x)=3sqrt{x}-\frac{2}{x^{2}}). (f(x)=)

Explanation:

Step1: Rewrite the function

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

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 $3\times\frac{1}{2}x^{\frac{1}{2}-1}=\frac{3}{2}x^{-\frac{1}{2}}$. For the second term $-2x^{-2}$, its derivative is $-2\times(-2)x^{-2 - 1}=4x^{-3}$.

Step3: Write the final derivative

Combining the derivatives of the two terms, $f^\prime(x)=\frac{3}{2\sqrt{x}}+\frac{4}{x^{3}}$.

Answer:

$\frac{3}{2\sqrt{x}}+\frac{4}{x^{3}}$