Question

usando la regla de la cadena resolver la sig derivada​

Answer 1

Respuesta: y'(x) = [6x√(x+1) + 5x + 4] / {[4√(x+1)][x+√(x+1)]^(1/2)}

Explicación paso a paso:

y(x)  = x . [x + (x + 1)^(1/2)]^(1/2)

Sea  G(x)  = x  y  H(x)  = [x + (x + 1)^(1/2)]^(1/2)

y'(x)  = G'(x). H(x)  +  G(x). H'(x).  Entonces:

y'(x)=1.[x+(x + 1)^(1/2)]^(1/2)] +x{1/2[x + (x + 1)^(1/2)]^(-1/2)][1+(1/2)(x+1)^(-1/2)]

= [6x√(x+1) + 5x + 4] / {[4√(x+1)][x+√(x+1)]^(1/2)}