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

Jaden Easton

Answered question

2021-10-20

Find the first and second derivatives

y = - x^{2} + 3

Cullen

Skilled2021-10-21Added 89 answers

Step 1
The given function here is,

y = - x^{2} + 3

The first derivative of y is given by,

\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 \cdot x^{2 - 1}) + 0

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

...(1)
Thus the first derivative of y is,

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

Step 2
The second derivative of y is given by,

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

Now substituting the values of dy/dx from (1) in the above equation,

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

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

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

Thus the second derivative of y is,

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

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