"Find the first and second derivatives of the..." solved and explained

UkusakazaL

Answered question

2021-10-15

Find the first and second derivatives of the function.

h (t) = \sqrt{t} + 5 \sin t

bahaistag

Skilled2021-10-16Added 100 answers

Step 1
we have to find the first and the second derivative of the function.

h (t) = \sqrt{t} + 5 \sin t

Step 2

h (t) = \sqrt{t} + 5 \sin t

we will first find the first derivative

h^{'} (t) = \frac{d}{d t} (\sqrt{t} + 5 \sin t)

h^{'} (t) = \frac{1}{2 \sqrt{t}} + 5 \cos t

now we will find the second derivative

h^{″} (t) = \frac{d}{d t} (\frac{1}{2 \sqrt{t}} + 5 \cos t)

h^{″} (t) = \frac{1}{2} \frac{d}{d t} (t^{- \frac{1}{2}}) + 5 \frac{d}{d t} (\cos t)

h^{″} (t) = \frac{1}{2} (- \frac{1}{2} t^{- \frac{1}{2} - 1}) - 5 \sin t

h^{″} (t) = \frac{1}{2} (- \frac{1}{2} t^{- \frac{3}{2}}) - 5 \sin t

h^{″} (t) = - \frac{1}{4} t^{- \frac{3}{2}} - 5 \sin t

h^{″} (t) = - \frac{1}{4 t^{\frac{3}{2}}} - 5 \sin t

Jeffrey Jordon

Expert2022-03-24Added 2605 answers

Answer is given below (on video)

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