# Find the first and second derivatives of the function h(t)

Find the first and second derivatives of the function
$h\left(t\right)=\sqrt{t}+5\mathrm{sin}$
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Step 1
To Determine:
Find the first and second derivatives of the function
$h\left(t\right)=\sqrt{t}+5\mathrm{sin}$
Given: we have a function $h\left(t\right)=\sqrt{t}+5\mathrm{sin}$
Explanation: we will differentiate the given function
$h\left(t\right)=\sqrt{t}+5\mathrm{sin}$
${h}^{\prime }\left(t\right)={\frac{1}{2}}^{{t}^{\frac{1}{2}-1}}+5\mathrm{cos}$
Step 2
${h}^{\prime }\left(t\right)={\frac{1}{2}}^{{t}^{\frac{1}{2}-1}}+5\mathrm{cos}$
Again differentiating we have
$h{}^{″}\left(t\right)=\frac{1}{2}\left(-\frac{1}{2}\right){t}^{-\frac{1}{2}-1}-5\mathrm{sin}$
$=-\frac{1}{4}{t}^{\frac{-3}{2}}-5\mathrm{sin}$