NCERT Class 12 · Ch 5 Exercise 5.5 · Q16
NCERT Class 12 Maths · Chapter 5 Continuity And Differentiability · Exercise 5.5 Question 16
Differentiate f(x)=(1+x)(1+x²)(1+x⁴)(1+x⁸) and find f′(1).
💡 Concept Hints
- Identify the domain and the inner and outer functions, or the relevant one-sided limits.
- Apply the appropriate differentiation or limit rule, keep all chain factors, and check exceptional points.
✅ Step-by-Step Solution
Final Answer: \(15 x^{14} + 14 x^{13} + 13 x^{12} + 12 x^{11} + 11 x^{10} + 10 x^{9} + 9 x^{8} + 8 x^{7} + 7 x^{6} + 6 x^{5} + 5 x^{4} + 4 x^{3} + 3 x^{2} + 2 x + 1\); f′(1)=120.
- The geometric product equals 1+x+x²+⋯+x¹⁵ (equivalently (x¹⁶−1)/(x−1) for x≠1).
- Differentiate the polynomial: f′=1+2x+⋯+15x¹⁴.
- At x=1, the sum is 1+2+⋯+15=15·16/2=120.
Master Chapter 5: Continuity And Differentiability
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Continuity And Differentiability.
← Previous Question
Find dy/dx if xʸ=e^(x−y).
Next Question →Differentiate (x²−5x+8)(x³+7x+9) by (i) product rule, (ii)…
All Questions in Continuity And Differentiability — Exercise 5.5
Related Questions in Continuity And Differentiability
Class 12 Continuity And Differentiability · Mcq Single Correct
For k<0, define f(x)=(1−cos(kx))/(x sin x) for nonzero x near 0, and f(0)=1/2. Find k for…
Class 12 Continuity And Differentiability · Mcq Single Correct
Near π/2, f(x)=k cos x/(π−2x) for x≠π/2 and f(π/2)=3. Find k for continuity.
Class 12 Continuity And Differentiability · Mcq Single Correct
Find the full set of real inputs excluded from the natural domain of cot x (its poles).
Class 12 Continuity And Differentiability · Mcq Single Correct
How many real inputs are excluded from the original formula f(x)=(x−1)/[x(x²−1)]?
Class 12 Continuity And Differentiability · Mcq Single Correct
For x≠0, f(x)=(e^(3x)−e^(−5x))/x, and f(0)=k. Find k for continuity at 0.
Class 12 Continuity And Differentiability · Mcq Single Correct
Let f(x)=x/|x| for x<0 and f(x)=−1 for x≥0. What is its complete continuity set?