Answer:
1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x
Step-by-step explanation:
f(x) = sin (tan^-1 (ln(x)))
u substitution
d/du (sin u) * du /dx
cos (u) * du/dx
Let u =(tan^-1 (ln(x))) du/dx =d/dx (tan^-1 (ln(x)))
v substitution
Let v = ln x dv/dx = 1/x
d/dv (tan ^-1 v) dv/dx
1/( v^2+1) * dv/dx
=1/(ln^2x +1) * 1/x
Substituting this back in for du/dx
cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x
We know that cos (tan^-1 (a)) = 1/ sqrt(1+a^2)
cos (tan^-1 (ln(x)) * 1/(ln^2x +1) * 1/x
1/ sqrt(1+ln^2(x)) * 1/(ln^2x +1) * 1/x
Answer:
The measures of two angles are 2x⁰ and (3x + 20)⁰. What is the measure of each angle if x = 14?
b 28 and 62
Answer:
90 and 30 liters
Step-by-step explanation:
1) if solution of 20% is 'x' and of 60% is 'y' liters, then
2) the pure chlorine is: for solution of 20% - 0.2x, for solution of 60% - 0.6y and
3) the mix of the two solutions is 120=x+y.
4) using these items it is possible to make up the system of two equations:
5) finally, x=90 liters of 20%; y=30 liters of 60% solution.
