Answered: "Find the first and second derivatives. y=6x2−10x−5x−2"

Elleanor Mckenzie

Answered question

2021-05-05

Find the first and second derivatives.

y = 6 x^{2} - 10 x - 5 x^{- 2}

Benedict

Skilled2021-05-06Added 108 answers

Step 1
We use the power rule to find the first derivative.
Power rule:

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

y = 6 x^{2} - 10 x - 5 x^{- 2}

\frac{d y}{d x} = \frac{d}{d x} (6 x^{2} - 10 x - 5 x^{- 2})

\frac{d y}{d x} = 6 (2 x) - 10 (1) - 5 (- 2) x^{- 2 - 1}

\frac{d y}{d x} = 12 x - 10 + 10 x^{- 3}

Step 2
Use power rule again to find the second derivative.

\frac{d y}{d x} = 12 x - 10 + 10 x^{- 3}

\frac{d^{2} y}{{d x}^{2}} = \frac{d}{d x} (12 x - 10 + 10 x^{- 3})

\frac{d^{2} y}{{d x}^{2}} = 12 (1) - 0 + 10 (- 3) x^{- 3 - 1}

\frac{d^{2} y}{{d x}^{2}} = 12 - 30 x^{- 4}

Answer:

\frac{d y}{d x} = 12 x - 10 + 10 x^{- 3}

\frac{d^{2} y}{{d x}^{2}} = 12 - 30 x^{- 4}

Jeffrey Jordon

Expert2021-11-24Added 2605 answers

Answer is given below (on video)

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