"Find the first and second derivative s=5t3−3t5" was answered by our experts

korporasidn

Answered question

2021-12-02

Find the first and second derivative

s = 5 t^{3} - 3 t^{5}

Answer & Explanation

Zachary Pickett

Beginner2021-12-03Added 17 answers

Step 1
The given function is,

s = 5 t^{3} - 3 t^{5}

Using the power rule of derivative,

\frac{d}{d x} (x^{n}) = n x^{n - 1}

Step 2
Finding the first derivative,

s^{'} = \frac{d}{d t} (s)

= \frac{d}{d t} (5 t^{3} - 3 t^{5})

= \frac{d}{d t} (5 t^{3}) - \frac{d}{d t} (3 t^{5})

= 5 \frac{d}{d t} (t^{3}) - 3 \frac{d}{d t} (t^{5})

= 5 (3 t^{2}) - 3 (5 t^{4})

s^{'} = 15 t^{2} - 15 t^{4}

Step 3
Finding the second derivative of the function,

s^{″} = \frac{d}{d t} (s^{'})

= \frac{d}{d t} (15 t^{2} - 15 t^{4})

= \frac{d}{d t} (15 t^{2}) - \frac{d}{d t} (15 t^{4})

= 15 \frac{d}{d t} (t^{2}) - 15 \frac{d}{d t} (t^{4})

= 15 (2 t) - 15 (4 t^{3})

s^{″} = 30 t - 60 t^{3}

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