Sheriff Oluwatofunmi

Question

f(x)=xcosh−1(x3)−√x2−9f(x)=xcosh-1(x3)-x2-9

then f'(5)

Answer 1

Given:

f(x) = x cosh^-1( x³ ) - √( x² - 9 )

Find:

f ' (5) = ?

Solution:

f ' (x) = d/dx ( f(x) )

f ' (x) = d/dx ( x cosh^-1( x³ ) - √( x² - 9 ) )

f ' (x) = d/dx ( x cosh^-1( x³ ) ) - d/dx ( √( x² - 9 ) )

f ' (x) = cosh^-1( x³ ) * d/dx (x) + x * d/dx ( cosh^-1( x³ ) ) - 2x / √( x² - 9 )

f ' (x) = cosh^-1( x³ ) + x [ (d/dx ( x³ )) / √( ( x³ )² - 1 ) ] - 2x / √( x² - 9 )

f ' (x) = cosh^-1( x³ ) + 3x³ / √( x⁶ - 1 ) - 2x / √( x² - 9 )

f ' (5) = cosh^-1( 5³ ) + 3*5³ / √( 5⁶ - 1 ) - 2*5 / √( 5² - 9 )

f ' (5) = cosh^-1( 125 ) + 3*125 / √( 15625 - 1 ) - 10 / √( 25 - 9 )

f ' (5) = cosh^-1( 125 ) + 375 / √( 15624 ) - 10 / √( 16 )

f ' (5) = cosh^-1( 125 ) + 375 / ( 6 * √( 434 ) ) - 10 / 4

f ' (5) = cosh^-1( 125 ) + 125 / ( 2 * √( 434 ) ) - 5 / 2

f ' (5) = cosh^-1( 125 ) + [ 5 ( 25 √( 434 ) - 434 ) ] / 868

f ' (5) ≈ 6.0215

I hope this helps! I know text answers can be hard to read sometimes but if you do have any questions, comments, or concerns, don't be afraid to post it in the comments.