Найдите производную 1) 90 2) - 10х 3) п/х 4) ×^5 5) 7×^3 6) (×-6)^4 7) (7-5х)^2 8) -...

Question

Найдите производную
1) 90
2) - 10х
3) п/х
4) ×^5
5) 7×^3
6) (×-6)^4
7) (7-5х)^2
8) - 4/х^2
9) 1/(х-6)^2
10) sin x/4

Answer 1

1) (90)' = 0.
2) (-10x)' = -10.
3) (п/x)' = (п)' * x - п * (x)' / x² = 0 - п/x² = -п/x².
4) (x^5)' = 5x^4.
5) (7x³)' = 7 * 3x² = 21x².
6) ((x^(-6))^4)' = x^(-24) = -24x^(-25).
7) ( (7 - 5x)² )' = -5 * 2(7 - 5x) = -10(7-5x) = -70 + 50x = 50x - 70.
8) (-4/x²)' = (-4)' * x² - (-4) * (x²)' / (x²)² = 8x / x^4 = 8 / x³.
9) (1 / (x-6)²)' = (1)' * (x-6)² - 1 * ((x-6)²)' / (x-6)^4 = 2(x-6) / (x-6)^4 = 2 / (x-6)³.
10) (sin x/4)' = 1/4 * cos x/4.