Question

If differentiation is represented by $d\left(\right)$, then $d\left(f\right(x\left)g\right(x\left)\right)$ is given by

• A. $d\left(f\right(x\left)\right)\times d\left(g\right(x\left)\right)$
• B. $d\left(f\right(x\left)\right)g\left(x\right)+f\left(x\right)d\left(g\right(x\left)\right)$
• C. $d\left(f\right(x\left)\right)+d\left(g\right(x\left)\right)$
• D. $d\left(f\right(x\left)\right)-d\left(g\right(x\left)\right)$

Answer 1

The correct option is B $d\left(f\right(x\left)\right)g\left(x\right)+f\left(x\right)d\left(g\right(x\left)\right)$

$f\left(x\right)g\left(x\right)$ is a product of two functions $f\left(x\right)$ and $g\left(x\right)$.
Using product rule, $d\left(f\right(x\left)g\right(x\left)\right)=d\left(f\right(x\left)\right)g\left(x\right)+f\left(x\right)d\left(g\right(x\left)\right)$