Question

3. f(x)=√4x encontrar la tercera derivada​
ayuda porfa ​

Answer 1

Respuesta:

f(x)=√(4x)

f'(x) = d/dx[√(4x) ] , √(4x)=√(4)*√(4)=2√(x)

Por ende:

f'(x)=d/dx[2√(x)]

f'(x)=2*d/dx[√(x) ]

f'(x)=2*1/2x^(1/2-1)

f'(x)=(2(1/2))x^(-1/2)

f'(x)=1x^(-1/2)

f'(x)=1/[√(x) ]

d/dx[ f'(x)] = d/dx[1/√(x) ] ; 1/√(x) = x^(-1/2)

Por lo que:

d/dx[f'(x)]= d/dx[x^(-1/2)]

f''(x)= -1/2*(x)^(-1/2-1)

f''(x)= -1/2*x^(-3/2)

f''(x)= -1/2*1/√((x)^3)  ; √((x)^3)=√((x)^2)*√(x) y √((x)^2)*√(x) = x√(x)

Entonces:

f''(x) = -1/2*1/(x√(x))

f''(x) = -1/(2(x√(x))

d/dx[f''(x)]= d/dx[-1/(2(x√(x)) ] ; -1/(2(x√(x)) = -1/2*x^(-3/2)

d/dx[f''(x) ] = d/dx [ -1/2*x^(-3/2) ]

f'''(x) = -1/2*d/dx[ x^(-3/2) ]

f'''(x)= ((-3/2((-1/2))x^(-3/2-1)

f'''(x) = 3/4*x^(-5/2)

f'''(x)= 3/(4(x^(5/2))

Espero ello te sirva

Good bye.

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