14\ ChemActivity G1A The Maxwell-Boltzmann Speed Distribution Law\ Critical Thinking Questions\ 4. Take the natural logarithm of each side of eqn (1) and then differentiate the resulting equation with respect to

v_(x)

.\

lnF(v)=lnf(v_(x))f(v_(y))f(v_(z))

\ 5. Use the chain rule to show that\

(dellnF(v))/(delv_(x))

\ If

v=\\\\sqrt(v_(x)^(2)+v_(y)^(2)+v_(z)^(2))

find

(delv)/(delv_(x))

.\ Use the results of CTQ 6 and equation (3) to show that\

(1)/(v)(dlnF(v))/(dv)=(1)/(v_(x))(dlnf(v_(x)))/(dv_(x))

14 ChemActivity G1A The Maxwell-Boltzmann Speed Distribution Law Critical Thinking Questions 4. Take the natural logarithm of each side of eqn (1) and then differentiate the resulting equation with respect to vx. lnF(v)=lnf(vx)f(vy)f(vz) 5. Use the chain rule to show that vxlnF(v))y,z=dvdlnF(v)vxv)y,z=dvxdlnf(vx) 6. If v=vx2+vy2+vz2 find vxv)y,z. 7. Use the results of CTQ 6 and equation (3) to show that v1dvdlnF(v)=vx1dvxdlnf(vx)