derivativesselfreview

derivativesselfreview - Look over this review sheet. Ask...

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Unformatted text preview: Look over this review sheet. Ask questions on Thursday. This is just for your review and does not have to be turned in. Name: ________________ Geol 351 Geomath Derivative review sheet Basic Differentiation Rules Relationship Rule dy Given y ax n ; = = anx n −1 dx dy df dg = + dx dx dx Given y = g ( x); f ( x) + dy dg df Given y f ( x) g ( x);= f = +g dx dx dx dy df dh Given y = f= (h( x)); dx dh dx Given y = f ( x) dy = ; g ( x) dx g df dg −f dx dx 2 g dy dh Given y = a e h ( x ) = ae h ( x ) ; dx dx ________________ ________________ ________________ ________________ ________________ ________________ General rule for differentiating the natural log (ln) dy 1 = ln( x); Given y = dx x dy 1 dh Given y = (application of the chain rule to differentiation of logs) = ln( h); dx h dx Derivatives of trig functions d cos θ = − sin θ dθ d sin θ = cos θ dθ d tan θ d sin θ … = dθ dθ cos θ Some additional practice (potential flash card candidates?) What are the derivatives of the following? 1 + 6t _____________ 4 x 2 + 2 x3 _____________ (1 + 2 z )3 _____________ 1 + 5x2 _____________ ( z + 7z ) 2 1 3 _____________ α = x 2 .e x _____________ y = 3ω 2 . sin(ω ) ω is the independent variable _____________ z = x.cos(x) + x 2 . tan( x) _____________ B = 3σ 4 . ln(σ ) + 17σ 2 σ is the independent variable _____________ ...
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This document was uploaded on 02/29/2012.

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derivativesselfreview - Look over this review sheet. Ask...

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