Can anyone explain me u/v method formula with example ?
Answers
Answer:
Ultraviolet radiation lies between wavelengths of about 400 nanometres (1 nanometre [nm] is 10−9 metre) on the visible-light side and about 10 nm on the X-ray side, though some authorities extend the short-wavelength limit to 4 nm. In physics, ultraviolet radiation is traditionally divided into four regions: near (400–300 nm), middle (300–200 nm), far (200–100 nm), and extreme (below 100 nm). Based on the interaction of wavelengths of ultraviolet radiation with biological materials, three divisions have been designated: UVA (400–315 nm), also called black light; UVB (315–280 nm), responsible for the radiation’s best-known effects on organisms; and UVC (280–100 nm), which does not reach Earth’s surface.
Answer:
formula: d(u/v)/dx= (v.du/dx-u.dv/dx)/v²
if u=x²+3x and v=x³+6x²
sol: du/dx=2x+3 and dv/dx=3x²+12x
put all these values in above formula
d[(x²+3x)/(x³+6x²)]/dx=[(x³+6x²×2x+3)-(x²+3x×3x²+12x)]/(x³+6x²)
=[(2x⁴+3x³+12x³+18x²)-(3x⁴+12x³+9x³+36x²)]/(x^6+36x⁴+12x^5)
=[2x⁴+15x³+18x²-3x⁴-21x³-36x²]/x²(x⁴+36x²+12x³)
=(-x⁴-6x³-18x²)/x²(x⁴+36x²+12x³)
=-x²(x²+6x+18)/x²(x⁴+36x²+12x³)
= -(x²+6x+18)/(x⁴+36x²+12x³)