Question

find h(t) if h(t) = \frac{9}{t^{2/5}} - \frac{4}{t^{1/2}}. h(t)=□

Explanation:

Step1: Rewrite the function

Rewrite $h(t)$ as $h(t)=9t^{-\frac{2}{5}}-4t^{-\frac{1}{2}}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y'=anx^{n - 1}$. For the first term, when $a = 9$ and $n=-\frac{2}{5}$, the derivative of $9t^{-\frac{2}{5}}$ is $9\times(-\frac{2}{5})t^{-\frac{2}{5}-1}=-\frac{18}{5}t^{-\frac{7}{5}}$. For the second term, when $a = - 4$ and $n=-\frac{1}{2}$, the derivative of $-4t^{-\frac{1}{2}}$ is $-4\times(-\frac{1}{2})t^{-\frac{1}{2}-1}=2t^{-\frac{3}{2}}$.

Answer:

$-\frac{18}{5t^{\frac{7}{5}}}+\frac{2}{t^{\frac{3}{2}}}$