3rd one please solve it
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Hope This Helps You!!
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The another way to solve this problem is to apply the product rule directly if you r unable to make an identity like @bellastark1 did .
f(x) = (1+x)(1+x^2)(1+x^4)(1+x^8)
so apply the product rule
f'(x) = (1+x^2)(1+x4)(1+x^8) d/dx(1+x) + (1+x)(1+x^4)(1+x^8) d/dx(1+x^2)
+ (1+x)(1+x^2)(1+x^8) d/dx(x^4) + (1+x)(1+x^2)(1+x^4) d/dx(x^8)
=> (1+x)(1+x^2)(1+x^8) (1) + (1+x)(1+x^4)(1+x^8) (2x) +(1+x)(1+x^2)(1+x^8)4x^3+(1+x)(1+x^2)(1+x^4) ( 8x^7)
now put x = 1 to find f'(1)
8 + 16 + 32 + 64
=> 120
f(x) = (1+x)(1+x^2)(1+x^4)(1+x^8)
so apply the product rule
f'(x) = (1+x^2)(1+x4)(1+x^8) d/dx(1+x) + (1+x)(1+x^4)(1+x^8) d/dx(1+x^2)
+ (1+x)(1+x^2)(1+x^8) d/dx(x^4) + (1+x)(1+x^2)(1+x^4) d/dx(x^8)
=> (1+x)(1+x^2)(1+x^8) (1) + (1+x)(1+x^4)(1+x^8) (2x) +(1+x)(1+x^2)(1+x^8)4x^3+(1+x)(1+x^2)(1+x^4) ( 8x^7)
now put x = 1 to find f'(1)
8 + 16 + 32 + 64
=> 120
kaharil:
tnx
;)
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