3)
dxdyβ=12dxdβeβ2xβ=12dxdβeβ2xβΓdxdβ(2βxβ) (chain rule to differentiate on)
=12Γe2βxβΓ2β1βdxdyβ=β62βxβ (equation of the radiant)
at x=2,dxdyβ=β6e2β2β=eβ6β
at x=4,dxdyβ=β6e2β4β=e2β6β
gradient at x=2 is eβ6β
gradient at x=4 is e2β6β
4)
dxdyβ=10dxdβlog(3x)=10Γln(10)1βΓ3x1βΓ3Γ1dxdyβ=xln(10)10β (chain rule to differentiate on)
dxdyβ=xln(10)10β (equation of the radiant)
at x=2,dxdyβ=2ln(10)10β=ln(10)5β
at x=8,dxdyβ=8ln(10)10β=4ln(10)5β
gradient at x=2 is ln(10)5β
gradient at x=8 is 4ln(10)5β
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