Maths · Differentiation of the sum, difference, product and quotient of two functions
If =\boldsymbol{a} \boldsymbol{x}+ \) then = \)
If \( \frac{\boldsymbol{d}}{\boldsymbol{d} \boldsymbol{x}}\left(\frac{1+\boldsymbol{x}^{2}+\boldsymbol{x}^{4}}{1+\boldsymbol{x}+\boldsymbol{x}^{2}}\right)=\boldsymbol{a} \boldsymbol{x}+ \) \( b, \) then \( (a, b)= \)
- A. (-1,2)
- B. (-2,1)
- C. (2,-1)
- D. (1,2)
Step-by-step solution
Simplify the rational function: (1+x^2+x^4)/(1+x+x^2) = 1 - x + x^2. Then differentiate: d/dx (1 - x + x^2) = 2x - 1, which matches a x + b with a = 2 and b = -1.