Get the answer to "f(x)=(8x−1)(x2+4x+7)(x3−5) Find the derivatives."

College
Calculus and Analysis
Differential Calculus
Derivatives

iohanetc

Answered question

2021-02-24

f (x) = (8 x - 1) (x^{2} + 4 x + 7) (x^{3} - 5)

Find the derivatives.

Answer & Explanation

Nathanael Webber

Skilled2021-02-26Added 117 answers

Given,
$f (x) = (8 x - 1) (x^{2} + 4 x + 7) (x^{3} - 5)$
On simplification, we get
$f (x) = (8 x^{3} + 32 x^{2} + 56 x - x^{2} - 4 x - 7) (x^{3} - 5)$
$= 8 x^{6} + 32 x^{5} + 56 x^{4} - x^{5} - 4 x^{4} - 7 x^{3} - 40 x^{3} - 160 x^{2} - 280 x + 5 x^{2} + 20 x + 35$
$= 8 x^{6} + 31 x^{5} + 52 x^{4} - 47 x^{3} - 155 x^{2} - 260 x + 35$
Now differentiating with respect to x, we get
$f^{'} (x) = 8 (6 x^{5}) + 31 (5 x^{4}) + 52 (4 x^{3}) - 47 (3 x^{2}) - 155 (2 x) - 260 (1) + 0$
$[\frac{d (x^{n})}{d x} = n x^{n - 1} \frac{d (c)}{d x} = 0, c \in R]$
$= 48 x^{5} + 155 x^{4} + 208 x^{3} - 141 x^{2} - 310 x - 260$

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