Question

Найти производные заданных функций
y=(4x^3+(3/(x^3√x))-2)^5
y=ln 6√((x^6-1)/(6x+5))^7
y=arctg√(x-1)
y=2^(x^2+1)-x*sin 4x

 

Answer 1

1) 5(4x^3+3*x^(-3,5)-2)^4*(12x^2-3*3,5x^(-4,5))=

=15(4x^3+3*x^(-3,5)-2)^4*(4x^2-3,5x^(-4,5))

2)((6x+5)/(x^6-1))^(3,5)*3,5*(x^6-1)/(6x+5))^(2,5)*(6x^5*(6x+5)-6*(x^6-1))/(6x+5)^2=

=21*(6x^6+5x^5-1)/(x^6-1)*(6x+5)

3)1/(2sqrt(x-1))*1/(1+(x-1))=1/(2xsqrt(x-1))

4)2^(x^2+1)*ln2*2x-sin4x-4xcos4x