Find `f'' (1) if f(x) = 2(2^(x))`

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lemjay | High School Teacher | (Level 3) Senior Educator

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First, determine f'(x). Apply the formula `(a^u)'=lna *a^u *u'` .


`f'(x)=2* ln2*2^x*x'`



Then, take the derivative of it again to get f"(x).




Now that the second derivative is know, solve for f"(1). So, plug-in x=1.




Hence, `f"(1)=4(ln2)^2` .

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aruv | High School Teacher | (Level 2) Valedictorian

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`ln(f(x))=ln(2)+xln(2)`      (i)

Differentiate (i) with respect to x ,



Differentiate (ii) with respect to x again,

`f''(x)=ln(2)f'(x)`             (iii)

Substitute value of f'(x) from (ii) in (iii), we have