Explained: "Find the first and second derivatives y=−3x9−1" - Plainmath

nicekikah

Answered question

2021-09-21

Find the first and second derivatives

y = - 3 x^{9} - 1

Answer & Explanation

un4t5o4v

Skilled2021-09-22Added 105 answers

Step 1
Given expression:

y = - 3 x^{9} - 1

Differentiate both sides with respect to x.
Use the differentiation formula

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

\frac{d y}{d x} = - 3 \cdot 9 x^{8} - 0

= - 27 x^{8}

Again differentiate both sides with respect to x.

\frac{d^{2} y}{{d x}^{2}} = - 27 \cdot 8 x^{7}

= - 216 x^{7}

Step 2
The answer is:
The first derivative:

\frac{d y}{d x} = - 27 x^{8}

The second derivative:

\frac{d^{2} y}{{d x}^{2}} = - 216 x^{7}

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