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# Calculus

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## Sara Martinez

on 29 May 2013

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#### Transcript of Calculus

Chain Rule Calculus Derivatives Trig Functions Chain Rule f(x)=(4x+2)²
f'(x)=2(4x+2)(4)
f'(x)=8(4x+2) f(x)=2sin(4x-2)
f'(x)=2cos(4x-2)(4)
f'(x)=8cos(4x-2) Cosine Trig Function f(x)=cos(23x)
f'(x)=-sin(23x)(23)
f'(x)=-23sin(23x) f(x) = 1/u
f'(x) = 1(u^(-1))
f'(x) = -u F(x) = (f · g)(x)

(du/dx) f(g(u))=f'(g(u))g'(u)

dy/dx = (dy/du)(du/dx) Sine Trig Function Chain Rule f(x)=2(3x+5)²
f'(x)=2*2(3x+5)(3)
f'(x)=4(3x+5)(3)
f'(x)=12(3x+5) f(x) = f(g(x))²
f'(x) =2f(g(x))g'(x) f(x) = sin^-1u
f'(x) = 1/sqrt 1-u² Product Rule d/dx = u'(x)g(x) + u(x)g'(x) Exponential f(u) = e^u
f'(u) = e^u f(x) = Sin^-1(2x^3)
f'(x) = 1/sqrt 1-(2x)²(2)
f'(x) = 2/sqrt 1 - 2x²(2)
f'(x) = 2/sqrt 1 - 4x² Sin Inverse Trig Function
Full transcript