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The function g(x)=ln(f(x)) passes through the origin. Show why the derivatives of f(x) and g(x) are equal when x = 0. Show all your work.

The function gxlnfx passes through the origin Show why the derivatives of fx and gx are equal when x 0 Show all your work class=

Respuesta :

MathPhys

Step-by-step explanation:

g(x) = ln(f(x))

Take derivatives of both sides.

g'(x) = 1/f(x) f'(x)

g(x) passes through the origin, so g(0) = 0:

g(0) = 0

ln(f(0)) = 0

f(0) = 1

Therefore:

g'(0) = 1/f(0) f'(0)

g'(0) = 1/1 f'(0)

g'(0) = f'(0)

amna04352

Answer:

Since at x = 0, g(x) = 0

ln(f(x)) = 0

f(x) = e^0 = 1

At x = 0, f(x) = 1

g'(x) = (1/f(x)) × f'(x)

At x = 0,

g'(x) = (1/1) × f'(x)

g'(x) = f'(x)

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