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worksheet_lab3_fall2011

# worksheet_lab3_fall2011 - • f 1 x = 3 x 2 • f 2 x = sin...

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Mathematics 115 – Fall ’11 Worksheet on differentiation Contents: product rule quotient rule (1) Find the derivative of the following functions using the product rule. f 1 ( x ) = x (2 x + x 2 ) f 2 ( x ) = x 3 ln( x ) f 3 ( x ) = sin( x )(cos( x ) + 1) f 4 ( x ) = x 3 e x f 5 ( x ) = ( x 4 + 3 x 3 )( x + 3 x 2 ) f 6 ( x ) = ln( x ) e x f 7 ( x ) = sin( x )( x 2 + 1) f 8 ( x ) = cos( x ) + x sin( x ) f 9 ( x ) = 5 x ln( x ) + x 5 (2 + x ) f 10 ( x ) = 5 sin( x ) - x 2 (cos( x ) + 6 sin( x )) f 11 ( x ) = x 10 ( x 5 - 4 x 3 ) f 12 ( x ) = 4(cos( x ) + x ) e x 1

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(2) Find the derivative of the following functions using the quotient rule.
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Unformatted text preview: • f 1 ( x ) = 3 x 2 • f 2 ( x ) = sin( x ) cos( x ) • f 3 ( x ) = x 2 + 5 x + 7 x 2-1 • f 4 ( x ) = log(3 x ) x + 1 • f 5 ( x ) = t cos t + t (sin( t )) 2 cos t • f 6 ( x ) = 1-t 1 3 1 + t 1 3 • f 7 ( x ) = t (csc t )(1 + cos t ) • f 8 ( x ) = e 2 x e 1 3 log x • f 9 ( x ) = x 2 sin x-x cos x x 2 sin x + x cos x • f 10 ( x ) = 3 x 2-12 ( x + 2)( x-2)...
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worksheet_lab3_fall2011 - • f 1 x = 3 x 2 • f 2 x = sin...

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