"Find the first and second derivatives s=7t4−4t7" was answered by students like you

Chesley

Answered question

2021-09-26

Find the first and second derivatives

s = 7 t^{4} - 4 t^{7}

Nathanael Webber

Skilled2021-09-27Added 117 answers

Step 1
The given function is,

s = 7 t^{4} - 4 t^{7}

To find the first and second derivative of the given function, we use the power rule of derivative

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

Finding the first derivative of the given function, we get

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

= \frac{d}{d t} (7 t^{4} - 4 t^{7})

= 7 (4 t^{3}) - 4 (7 t^{6})

= 28 t^{3} - 28 t^{6}

Hence, the first derivative of the given function is

28 t^{3} - 28 t^{6}

Step 2
Finding the second derivative of the function, we get

s^{″} = \frac{d}{d t} (s^{'})

= \frac{d}{d t} (28 t^{3} - 28 t^{6})

= 28 (3 t^{2}) - 28 (6 t^{5})

= 84 t^{2} - 168 t^{5}

Therefore, the second derivative of the given function is

84 t^{2} - 168 t^{5}

Jeffrey Jordon

Expert2022-03-13Added 2605 answers

Answer is given below (on video)

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