Question 1193579
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1.
{{{y= log(a,(x^3+2x-2))}}}

First change the log base a to "ln" (which is log base e) by 
replacing "log<sub>a</sub>" by "ln" and dividing by ln(a).

{{{y= ln(x^3+2x-2)/ln(a^"")}}}

{{{ln(a^"")*y=ln(x^3+2x-2)}}}

Use the ln derivative formula: "(The derivative of what the "ln" is of)
divided by what the "ln" is of.

{{{ln(a^"")expr(dy/dx)=(3x^2+2)/(x^3+2x-2)}}}

{{{dy/dx=(3x^2+2)/(ln(a)(x^3+2x-2))}}}

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2.
{{{y= ln^3(x^""+ sin(x))}}}

Write it so you can tell what's being raised to the 3rd power:

{{{y= (ln(x^""+ sin(x))^"")^3}}}

Use the power rule and the chain rule

{{{dy/dx= 3(ln(x^""+ sin(x))^"")^2*matrix(1,2,d/dx,(ln(x^""+ sin(x))^""))}}}

Use the ln derivative formula: "(The derivative of what the "ln" is of)
divided by what the "ln" is of.

{{{dy/dx= 3(ln(x^""+ sin(x))^"")^2*((1+cos(x))/(x+sin(x)))}}}

Simplify the appearance of the first factor by putting the 2
exponent immediately after the "ln"

{{{dy/dx= 3*ln^2(x^""+ sin(x))^""*((1+cos(x))/(x+sin(x)))}}}

Edwin</pre>