Turunan trigonometri

Turunan

4) f(x) =  cos x². sin² x

u= cos x² –> u' = – 2x sin x²

v = sin² x –> v' = 2 sin x cos x

f'(x)= u'v + uv'

f'(x) =  (-2 x sin x²)(sin² x) + (cos x²)(2 sin x cos x)

f'(x) =  - 2 x sin² x sin x² +  2 sin x cos x cos x²

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5) f(x) =[ (x² + 1) /(cos x)]⁴

u = (x² + 1) /(cos x) –> u' = (2x  cos x – (-sin x)(x²+1))/(cos² x)

du/dx = (2x cos x + (x²+ 1) sin x ) / (cos² x)

y= u⁴ –> dy/du = 4u³

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y' = dy/dx

dy/dx= dy/du. du/dx

y' = 4 u³ .  (2x cos x + (x²+ 1) sin x ) / (cos² x)

y' = 4 {(x² + 1 )/(cos x)}³ (2x cos x + (x²+ 1) sin x ) / (cos² x)

y' = 4(x²+1)³  (2x cos x + (x²+ 1) sin x )  / ( cos³ x cos² x)

y'  = 4(x²+1)³  (2x cos x + (x²+ 1) sin x )  / ( cos⁵ x)