Solved: "Higher-order derivatives Find f′(x), f″(x), and f′″(x) for..."

NompsypeFeplk

Answered question

2021-12-05

Higher-order derivatives Find f′(x), f″(x), and f′″(x) for the following functions

f (x) = 3 x^{3} + 5 x^{2} + 6 x

Aretha Frazier

Beginner2021-12-06Added 16 answers

Step 1
Definition used -
Power rule of derivative -

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

And we know that-

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

Step 2
Given -

f (x) = 3 x^{3} + 5 x^{2} + 6 x

Differentiating f(x) with respect to x-

f^{'} (x) = 3 (3 x^{2}) + 5 (2 x) + 6 (1)

= 9 x^{2} + 10 x + 6

Differentiating it again with respect to x-

f^{″} (x) = 9 (2 x) + 10 (1) + 0

=18x+10
Step 3
Differentiating again with respect to x-

f^{‴} (x) = 18 (1) + 0

=18

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