3 Qs: find f' for f = x^(lnx) / find tangent / find A for...

[Lime]

That I don't know how to solve.

1) If f(x) = x^(lnx), find f'(x)

2) Determine the x-coordinate of the point on the curve y = 8ln(x+1) where the tangent line is parallel to the line y = 2x+5.

3) If [(8x-11)] / [(x-2)(x-1)] = A/(x-2) + B/(x-1) , find the value of A.

 

[marcmtlca]

1) looks like it might the log differentiation

y=x^(ln x)

ln y = (ln x)(ln x)

y'/y= 2(ln x)/x

y'=y 2 (ln x ) /x

y' = 2 (ln x )x^(ln x) /x

 

[stapel]

2) What is the slope of y = 2x + 5? At what x-value(s) does y = 8 ln(x + 1) have a derivative with that value?

3) Multiply through by the common denominator. Multiply everything out, and equate coefficients. Solve the resulting system of equations for A.

Eliz.