Question: "Find the first and second derivatives. y=−x2+3"

Efan Halliday

Answered question

2021-05-04

Find the first and second derivatives.

y = - x^{2} + 3

gwibdaithq

Skilled2021-05-05Added 84 answers

Step 1
The given function is

y = - x^{2} + 3

.
Formula:

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

\frac{d}{d x} (f + g) = \frac{d f}{d x} + \frac{d g}{d x}

\frac{d}{d x} (k) = 0

where k is constant.

\frac{d}{d x} (k f) = k \frac{d}{d x} (f)

Step 2
Obtain the first derivative of y as follows.

y = - x^{2} + 3

\frac{d y}{d x} = \frac{d}{d x} (- x^{2} + 3)

= \frac{d}{d x} (- x^{2}) + \frac{d}{d x} (3)

= - \frac{d}{d x} (x^{2}) + \frac{d}{d x} (3)

= - 2 x^{2 - 1} + 0

= - 2 x^{1}

=-2x
Step 3
Obtain the second derivative as follows.

\frac{d y}{d x} = - 2 x

\frac{d^{2} y}{{d x}^{2}} = \frac{d}{d x} (\frac{d y}{d x})

= \frac{d}{d x} (- 2 x)

= - 2 \frac{d}{d x} (x)

= - 2 \times 1 x^{1 - 1}

= - 2 x^{0}

=-2

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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