Expert answers to "Find the derivatives of the given functions. p(x)=(x2+5x+2)(x4−x3+x2+x−2)"

College
Calculus and Analysis
Differential Calculus
Derivatives

BenoguigoliB

Answered question

2021-10-15

Find the derivatives of the given functions.

p (x) = (x^{2} + 5 x + 2) (x^{4} - x^{3} + x^{2} + x - 2)

Answer & Explanation

hosentak

Skilled2021-10-16Added 100 answers

Expand $p (x)$ first then apply power rule to find $p^{'} (x)$
Power rule: $\frac{d}{d x} (x^{n}) = n \cdot x^{n - 1}$
$p (x) = (x^{2} + 5 x + 2) (x^{4} - x^{3} + x^{2} + x - 2)$
$p (x) = x^{6} + 4 x^{5} - 2 x^{4} + 4 x^{3} + 5 x^{2} - 8 x - 4$
$p^{'} (x) = 6 x^{5} + 4 (5 x^{4}) - 2 (4 x^{3}) + 4 (3 x^{2}) + 5 (2 x) - 8$
$p^{'} (x) = 6 x^{5} + 20 x^{4} - 8 x^{3} + 12 x^{2} + 10 x - 8$
Answer: $p^{'} (x) = 6 x^{5} + 20 x^{4} - 8 x^{3} + 12 x^{2} + 10 x - 8$

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