find h(t) if h(t)=4/t^1/6 - 7/t^4/7.
find h(t) if h(t)=4/t^1/6 - 7/t^4/7.
Answer
Explanation:
Step1: Rewrite the function
Rewrite $h(t)$ as $h(t)=4t^{-\frac{1}{6}}-7t^{-\frac{4}{7}}$ using the rule $\frac{1}{x^n}=x^{-n}$.
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 $4t^{-\frac{1}{6}}$, its derivative is $4\times(-\frac{1}{6})t^{-\frac{1}{6}-1}=-\frac{2}{3}t^{-\frac{7}{6}}$. For the second term $-7t^{-\frac{4}{7}}$, its derivative is $-7\times(-\frac{4}{7})t^{-\frac{4}{7}-1}=4t^{-\frac{11}{7}}$.
Answer:
$h^\prime(t)=-\frac{2}{3}t^{-\frac{7}{6}} + 4t^{-\frac{11}{7}}$