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## Homework Statement

Function

f(x) = K

^{xL}

K= 1.78

L= -1.39

Problem 1: Find f'(x).

____________________

v= 0.89

w= 0.5

"v" and "w" are two points located on the x-axis.

Problem 2: Calculate f'(v).

____________________

Problem 3: Find the equation of the tangent line of f(x) over the point "w". The equation should be in this form y=Ax+B

____________________

Problem 1:This is how I worked out the differentiation:

f(x) = e

^{(ln 1.78)x-1.39}

Setting u=x

^{-1.39},

f'(x) = (K

^{u})'(u) * u'

(K

^{u})'(u) = (e

^{u ln K})' = ln K * e

^{u ln K}= ln K * K

^{u}

u' = Lx

^{L-1}= -1.39x

^{-2.39}

So,

f'(x) = ln 1.78(1.78

^{x-1.39}) * -1.39x

^{-2.39}

Is this correct?

Regarding the other problems, do I need f'(x) to solve these? I don't know where to start.

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