WkSheet1solutions

# WkSheet1solutions - number of minus signs 5 g x = x 3 sin...

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Solutions to Calculating Derivatives 1 2) f ( x ) = sin(3 x 2 + x ) + x 2 + 1 [sin(3 x 2 + x ) + x 2 + 1] 0 = [sin(3 x 2 + x )] 0 + [ x 2 + 1] 0 Sum Rule (S. R.) = [cos(3 x 2 + x )(6 x + 1)] + [( x 2 + 1) 1 2 ] 0 Chain Rule (C. R.) = [cos(3 x 2 + x )(6 x + 1)] + [( 1 2 ( x 2 + 1) - 1 2 )(2 x )] C. R. = cos(3 x 2 + x )(6 x + 1) + x ( x 2 + 1) - 1 2 Simplify 3) f ( x ) = x 3 tan( x 4 + x ) [ x 3 tan( x 4 + x )] 0 = [ x 3 ] 0 [tan( x 4 + x )] + [tan( x 4 + x )] 0 [ x 3 ] Product Rule (P. R.) = [3 x 2 ][tan( x 4 + x )] + [tan( x 4 + x )] 0 [ x 3 ] = [3 x 2 ][tan( x 4 + x )] + [sec 2 ( x 4 + x )(4 x 3 + 1)][ x 3 ] C. R. 4) f ( x ) = cos(sin( - x )) cos(cos( - 2 x 3 )) ± cos(sin( - x )) cos(cos( - 2 x 3 )) ² 0 = [cos(sin( - x ))] 0 [cos(cos( - 2 x 3 ))] - [cos(cos( - 2 x 3 ))] 0 [cos(sin( - x ))] (cos(cos( - 2 x 3 ))) 2 Q. R. = [( - sin(sin( - x )))(cos( - x ))( - 1)] · [cos(cos( - 2 x 3 ))] (cos(cos( - 2 x 3 ))) 2 - - [( - sin(cos( - 2 x 3 )))( - sin( - 2 x 3 ))( - 6 x 2 ))] · [cos(sin( - x ))] (cos(cos( - 2 x 3 ))) 2 C.R. The solution would not ﬁt on one line. No need to simplify. Make sure you have the right

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Unformatted text preview: number of minus signs. 5) g ( x ) = x 3 sin 2 (3 x 2 ) [ x 3 sin 2 (3 x 2 )] = [ x 3 ] [sin 2 (3 x 2 )] + [sin 2 (3 x 2 )] [ x 3 ] P. R. = [3 x 2 ][sin 2 (3 x 2 )] + [sin 2 (3 x 2 )] [ x 3 ] = [3 x 2 ][sin 2 (3 x 2 )] + [(2 sin(3 x 2 ))(cos(3 x 2 )(6 x )][ x 3 ] C. R. Feel free to ask me about the challenge question if you are curious. Can you ﬁnd a formula for the derivative of the product of three functions? We know: [ gh ] = [ g ] [ h ] + [ h ] [ g ] . What about: [ fgh ] =???...
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WkSheet1solutions - number of minus signs 5 g x = x 3 sin...

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