Unformatted text preview: and that the sine appears to be steepest where the cosine takes on its extreme values of 1 and1. Of course, now that we know the derivative of the sine, we can compute derivatives of more complicated functions involving the sine. EXAMPLE 4.2 Compute the derivative of sin( x 2 ). d dx sin( x 2 ) = cos( x 2 ) · 2 x = 2 x cos( x 2 ) . EXAMPLE 4.3 Compute the derivative of sin 2 ( x 35 x ). d dx sin 2 ( x 35 x ) = d dx (sin( x 35 x )) 2 = 2(sin( x 35 x )) 1 cos( x 35 x )(3 x 25) = 2(3 x 25) cos( x 35 x ) sin( x 35 x ) . Exercises Find the derivatives of the following functions. 1. sin 2 ( √ x ) ⇒...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Derivative, Slope, ........., Mathematical analysis

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