question 2\nfind the derivative of the function.\nh(t)=\\frac{t^{9}+7t^{5}+9t^{2}}{8t^{2}}\n\\(\\frac{7}{8}t^…

question 2\nfind the derivative of the function.\nh(t)=\\frac{t^{9}+7t^{5}+9t^{2}}{8t^{2}}\n\\(\\frac{7}{8}t^{6}+\\frac{21}{8}t^{2}+\\frac{9}{8}\\)\n\\(\\frac{7}{8}t^{7}+\\frac{21}{8}t^{3}+\\frac{9}{8}\\)\n\\(\\frac{1}{8}t^{7}+\\frac{21}{8}t^{3}\\)\n\\(\\frac{1}{8}t^{6}+\\frac{21}{8}t^{2}\\)

question 2\nfind the derivative of the function.\nh(t)=\\frac{t^{9}+7t^{5}+9t^{2}}{8t^{2}}\n\\(\\frac{7}{8}t^{6}+\\frac{21}{8}t^{2}+\\frac{9}{8}\\)\n\\(\\frac{7}{8}t^{7}+\\frac{21}{8}t^{3}+\\frac{9}{8}\\)\n\\(\\frac{1}{8}t^{7}+\\frac{21}{8}t^{3}\\)\n\\(\\frac{1}{8}t^{6}+\\frac{21}{8}t^{2}\\)

Answer

Explanation:

Step1: Simplify the function

First, divide each term in the numerator by $8t^{2}$: [h(t)=\frac{t^{9}}{8t^{2}}+\frac{7t^{5}}{8t^{2}}+\frac{9t^{2}}{8t^{2}}=\frac{1}{8}t^{7}+\frac{7}{8}t^{3}+\frac{9}{8}]

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. For the first term $\frac{1}{8}t^{7}$, its derivative is $\frac{1}{8}\times7t^{7 - 1}=\frac{7}{8}t^{6}$. For the second term $\frac{7}{8}t^{3}$, its derivative is $\frac{7}{8}\times3t^{3 - 1}=\frac{21}{8}t^{2}$. For the third term $\frac{9}{8}$ (a constant), its derivative is 0. So, $h^\prime(t)=\frac{7}{8}t^{6}+\frac{21}{8}t^{2}$.

Answer:

$\frac{7}{8}t^{6}+\frac{21}{8}t^{2}$