Question

Помогите производная...

Answer 1

1) y = 63

y' = (63)' = 0

2) y = x

y' = (x)' = 1

3) y = 12x

y' = 12 * (x)' = 12

4) y = x⁴

y' = (x⁴)' = 4x⁴⁻¹ = 4x³

5) y = 5x⁵ + 11

y' = 5(x⁵)' + 11' = 5 * 5x⁴ + 0 = 25x⁴

$6)y=\frac{1}{7}x^{7}+\frac{5}{6}x^{6}+\frac{1}{4}x^{4}+6\\\\y'=\frac{1}{7}(x^{7})'+\frac{5}{6}(x^{6})'+\frac{1}{4}(x^{4} )'+6'=\frac{1}{7}*7x^{6}+\frac{5}{6}*6x^{5}+\frac{1}{4}*4x^{3}+0}=x^{6}+5x^{5}+x^{3}\\\\7)y=(7x^{5}-7)(x^{2}-1)\\\\y'=(7x^{5}-7)'*(x^{2}-1)+(7x^{5}-7)*(x^{2}-1)'=35x^{4}*(x^{2}-1)+2x*(7x^{5}-7)=35x^{6}-35x^{4}+14x^{6}-14x=49x^{6}-35x^{4}-14x$

$8)y=\frac{3x^{4} }{(x^{2}+2)}\\\\y'=\frac{(3x^{4})'*(x^{2}+2)-3x^{4}*(x^{2}+2)'}{(x^{2}+2)^{2}}=\frac{12x^{3}*(x^{2}+2)-3x^{4}*2x}{(x^{2}+2)^{2}}=\frac{12x^{5}+24x^{3}-6x^{5}}{(x^{2}+2)^{2}}=\frac{6x^{5}+24x^{3}}{(x^{2}+2)^{2}}$