Posted by Anonymous on Sunday, January 25, 2009 at 12:57pm.
Differentiate the given function. Simplify the answer.
f(x) = 28x*ln√x + 42
f'(x) = 28*ln(x)^(1/2) + (1/(x^(1/2))*(1/2(x)^(-1/2)28x)
f'(x) = 28*ln(x)^(1/2) + (14x*x^(-1/2))/x^(1/2)
f'(x) = 28*ln(x)^(1/2) + (14x^(-1/2))/x^(1/2)
f'(x) = 28*ln(x)^(1/2) + (14x^(-1)
f'(x) = 28*ln(x)^(1/2) + 1/14x
... how do I simplify further to "14(1 + lnx)"??
Math - Derivatives - Damon, Sunday, January 25, 2009 at 1:09pm
28 x ln [sqrt (x+42)] ?maybe? I need more parentheses to understand.
[28 x/sqrt(x+42) ](1/2)x/sqrt(x+42) +28 ln(sqrt(x+42)]
14 x^2/(x+42) + 28 ln[sqrt(x+42]
Math - Derivatives - Anonymous, Sunday, January 25, 2009 at 1:27pm
The original equation is...
f(x) = (28x)(ln(sqrt(x)) + 42
Math - Derivatives - Damon, Sunday, January 25, 2009 at 3:35pm
Well then, the 42 is irrelevant for our purposes since its derivative is zero.
28 x (d/dx ln x^.5) + 28 ln x^.5
28 x [ (1/x^.5) .5 x^-.5 ] + 28 ln x^.5
28 x (.5/x) + 28 ln x^.5
14 + 28 ln sqrt x
Answer This Question
More Related Questions
- algebra - solve the following equation by clearing fractions show all work want ...
- math - which equation is equivalent to 5x-2(7x+1)=14x? why? a -9x-2=14x b -9xt1=...
- Science (Chemistry) - Hello DrBob222 Regarding the answer you gave me thank you ...
- Maths - find the equation of the perpendicular bisector of the line joining P(2...
- algebra - Andrew factored the expression 28x©ø-6x©÷-10x as 2x(14x©ø-3x©÷-5x) . ...
- algebra - solve the following equation by clearing fraction want to know if this...
- Algebra - Really need some help 1. 14x^2+4+3x-12x^2-3+11x A) 2x^2+7x+1 B) 2x^2+...
- ALGEBRA - If I divide 28x^3-30x^2-67x-21 BY 7x+3...will I get 4x^2-10x-21? THEN ...
- MATH - explain how to put 7y-14x=21 in slope intercept form. You want y=mx + b ...
- math - how do i do x2+12x+32 x2+12x = 14x+32 subtract 14x from each side 14x=32 ...