Question

Найдите производную функции :
$y = 12x {}^{5} - 10x {}^{4} + 4 \sqrt{x} - \frac{7}{x {}^{3} } - 2x + 11$
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Answer 1

Ответ:

${}\ \ \ \ \ \boxed{\ (x^{n})'=n\cdot x^{n-1}\ ,\ \ \ (C\cdot u)'=C\cdot u'}\\\\\\y=12x^5-10x^4+4\sqrt{x}-\dfrac{7}{x^3}-2x+11\\\\\\y=12x^5-10x^4+4x^{\frac{1}{2}}-7x^{-3}-2x+11\\\\\\y'=12\cdot 5x^4-10\cdot 4x^3+4\cdot \dfrac{1}{2}\, x^{-\frac{1}{2}}-7\cdot (-3x^{-4})-2=\\\\\\=60x^4-40x^3+\dfrac{2}{\sqrt{x}}+\dfrac{21}{x^4}-2$