ChainRule

ChainRule - h ( x ) at the point (ln( / 6) ,h (ln( / 6)))....

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Mathematics 115 – F2011 - Chain Rule Problems (1) Let h ( x ) = p sin( e x ). Find h 0 ( x ). h ( x ) = f ( g ( x )) where f ( u ) = u and g ( x ) = sin( e x ). Then h 0 ( x ) = f 0 ( g ( x )) · g 0 ( x ) Chain Rule = 1 2 ( g ( x )) - 1 / 2 · g 0 ( x ) E.P.R. applied to f ( u ) = u 1 / 2 = 1 2 (sin( e x )) - 1 / 2 · cos( e x ) · ( e x ) 0 Chain Rule applied to g ( x ) = cos( e x ) = e x cos( e x ) 2 p (sin( e x )) (2) Let h ( x ) = p sin( e x ). Find h (ln( π/ 6)). Find the equation of the tangent line to the graph of
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Unformatted text preview: h ( x ) at the point (ln( / 6) ,h (ln( / 6))). (3) Let y = ln(tan x ). Find dy dx . [You can either use the denition of tan x and properties of the logarithm function to rst simplify this, or use the derivative of the tan x .]...
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