Question

f(x) = (1 + x) (1 + x^{2}) (1 + x^{4}) (1 + x^{8}) द्वारा प्रदत्त फलन का अवकलज ज्ञात कीजिए और इस प्रकार f'(1) ज्ञात कीजिए।

Answer 1

f'(1)  =  120  यदि f(x)  = (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)

Step-by-step explanation:

f(x)  = (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)

f'x = (1 + x)'(1 + x²)(1 + x⁴)(1 + x⁸) + (1 + x)(1 + x²)'(1 + x⁴)(1 + x⁸) + (1 + x)(1 + x²)(1 + x⁴)'(1 + x⁸) + (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸)'

=> f'x = (1)(1 + x²)(1 + x⁴)(1 + x⁸) + (1 + x)(2x)(1 + x⁴)(1 + x⁸) + (1 + x)(1 + x²)(4x³)(1 + x⁸) + (1 + x)(1 + x²)(1 + x⁴)(8x⁷)

=>  f'x =  (1 + x)(1 + x²)(1 + x⁴)(1 + x⁸) (1/(1 + x)  + 2x/(1 + x²)  + 4x³/(1 + x⁴) + 8x⁷/(1 + x⁸) )

x = 1

=> f'(1)  = (1 + 1)(1 + 1) (1 + 1) (1 + 1) (1/(1+1)  + 2(1)(1 + 1)  4(1)/(1 + 1)  8(1)/(1 + 1))

=> f'(1)  =  2 * 2 * 2 * 2 ( 1/2  + 1  + 2  + 4)

=>  f'(1)  = 16 ( 15/2)

=>  f'(1)  =  120

और अधिक जानें :

sin(x²+5)"

brainly.in/question/15286193

sin (ax+b) फलन का अवकलन कीजिए

brainly.in/question/15286166