Question #16380

if y=(x+(x^2+m^2)^1/2)^n then dy/dx

Expert's answer

y'=(x+(x^2+m^2)^1/2)^n=(n(x+(x^2+m^2)^1/2))^(n-1))(x+(x^2+m^2)^1/2)'=

(n(x+(x^2+m^2)^1/2))^(n-1))(1+((x^2+m^2)^1/2)'=(n(x+(x^2+m^2)^1/2))^(n-1))(1+2x/2((x^2+m^2)^1/2)=(n(x+(x^2+m^2)^1/2))^(n-1))(1+x/((x^2+m^2)^1/2)

(n(x+(x^2+m^2)^1/2))^(n-1))(1+((x^2+m^2)^1/2)'=(n(x+(x^2+m^2)^1/2))^(n-1))(1+2x/2((x^2+m^2)^1/2)=(n(x+(x^2+m^2)^1/2))^(n-1))(1+x/((x^2+m^2)^1/2)

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