Solved: "Second derivatives Find d2ydx2 for the following functions...." - Plainmath

Kelly Nelson

Answered question

2021-12-07

Second derivatives Find

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

for the following functions.

y = 2 x^{2} + 2

Answer & Explanation

porschomcl

Beginner2021-12-08Added 28 answers

Step 1
The given function is

y = 2 x^{2} + 2

.
Step 2
Obtain the first derivative as shown below:

y = 2 x^{2} + 2

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

\frac{d y}{d x} = 2 (2 x) + 0

\frac{d y}{d x} = 4 x

Obtained the second derivative as shown below:

\frac{d^{2} y}{{d x}^{2}} = \frac{d}{d x} (4 x)

= 4 \frac{d}{d x} (x)

=4

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