NDA2018MathematicsDifferentiationActual
If u=e^ a x b x and v=e^ a x b x , then what is u d u d x +v d v d x equal to?
Options
- Aa e^ 2 a x
- B(a^2+b^2 ) e^ a x
- Ca b e ^ 2 ax
- D(a+b) e^ a x
Correct answer
A. a e^ 2 a x
Step-by-step solution
aligned & u d u d x +v d v d x =e^ a x b x [a e^ a x b x+b e^ a x b x ] & +e^ a x b x [a e^ a x b x-b e^ a x b x ] & =e^ 2 a x [a ^2 b x+b b x b x+ . & .a ^2 b x-b b x b x ] & =a e^ 2 a x aligned