Question

求下列函数的导数；y=2x-1/根号 x²+1y=(x+1)根号x²+1y=(x²-5）的立方+2（x²-5)²

Answer 1

y=2x-1/(x²+1)^0.5=(2x-1)(x²+1)^(-0.5)

y'=2*(x²+1)^(-0.5)+(-0.5*(2x-1)*(x²+1)^(-1.5)*2x)

=2/(x²+1)^0.5-(2x-1)*x/(x²+1)^1.5

=(2*(x²+1)-2x^2+x)/(x²+1)^1.5

=(2+x)/(x²+1)^1.5

y=(x+1)(x²+1)^0.5

y'=(x²+1)^0.5+0.5*(x+1)(x²+1)^(-0.5)*2x

=(x²+1)^0.5+x*(x+1)(x²+1)^(-0.5)

=((x²+1)+(x^2+x))/(x²+1)^0.5

=(2x²+x+1)/(x²+1)^0.5

y=(x²-5)^3+2(x²-5)²

y'=3*(x²-5)^2*2*x+2*2*(x²-5)*2*x

=6*x*(x²-5)^2+8*x*(x²-5)

=2*x*(3(x²-5)^2+4*(x²-5))

=2*x*(3(x^4-10x^2+25)+4*x²-20)

=2*x*(3*x^4-30x^2+75+4*x²-20)

=2*x*(3*x^4-26x^2+55)