Solution: We can simplify this problem using the rules of the logarithm function:
This is easier to integrate since ln(a) is constant and ln(x) has a familiar derivative.
Thus, d=-2 and c=-b, so the answer is:
c=-95
Wednesday, February 22, 2012
Differentiating the log function and log rules (Online calculus course test homework solutions)
Question: The second derivative of the function ln(ax^b) has a SECOND derivative that can be written in the form cx^d. What is the value of c if a=55 and b=95?
Solution: We can simplify this problem using the rules of the logarithm function:
=ln(a)+ln(x^b)=ln(a)+b*ln(x) "ln(a*x^b)=ln(a)+ln(x^b)=ln(a)+b*ln(x)")
This is easier to integrate since ln(a) is constant and ln(x) has a familiar derivative.
+b*ln(x)\Rightarrow y'=\frac{b}{x}\Rightarrow y''=-bx^{-2} "y=ln(a)+b*ln(x)\Rightarrow y'=\frac{b}{x}\Rightarrow y''=-bx^{-2}")
Thus, d=-2 and c=-b, so the answer is:
c=-95
Solution: We can simplify this problem using the rules of the logarithm function:
This is easier to integrate since ln(a) is constant and ln(x) has a familiar derivative.
Thus, d=-2 and c=-b, so the answer is:
c=-95
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