Find the derivative of f ( x ) = ( x 2 + 8 ) ( 8 x − 1 ) by first expanding the polynomials.Enter the fully simplified expression for f (x) after expanding the polynomials

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Find the derivative of   f  (  x  )  =  (      x    2    +  8  )  (  8  x  −  1  ) by first expanding the polynomials.Enter the fully simplified expression for f (x) after expanding the polynomials

Emaidedip6g · Accepted Answer

f  (  x  )  =  (      x    2    +  8  )  (  8  x  −  1  )find derivative=?We use the substitutions   u  =      x    2    +  8 and v=8x-1Now, use product rule            d      (      u      v      )              d      x        =  u            d      v              d      x        +  v            d      u              d      x          =  (      x    2    +  8  )      d          d      x        (  8  x  −  1  )  +  (  8  x  −  1  )      d          d      x        (      x    2    +  8  )Now, we differentiate  =  (      x    2    +  8  )  ×  (  8  )  +  (  8  x  −  1  )  ×  (  2  x  )    =  8      x    2    +  64  +  16      x    2    −  2  x    =  24      x    2    −  2  x  +  64    f  (  x  )  =  24      x    2    −  2  x  +  64Now, find f&#039;(x)=?  f  (  x  )  =  24      x    2    −  2  x  +  64differentiate with respect to x      f    ′    (  x  )  =  48  x  −  2

Find the derivative of f(x)=(x^2+8)(8x-1) by first expanding the polynomials. Enter the fully simplified expression for f(x) after expanding the polynomials

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