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5(-x^2tan^2(x)+sec(x)cos(x)(x^2sec^2(x)+2xtan(x)))/(sec^2(x)cos(x)) if x=5 

 Oct 6, 2016
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5(-x^2tan^2(x)+sec(x)cos(x)(x^2sec^2(x)+2xtan(x)))/(sec^2(x)cos(x)) if x=5 

 

\(\frac{5 ( -x^2tan^2(x) + sec(x)cos(x) (x^2sec^2(x)+2xtan(x)) ) }{ (sec^2(x) cos(x))} \\ =\frac{5 ( -x^2tan^2(x) + 1 (x^2sec^2(x)+2xtan(x)) ) }{ \frac{ cos(x)}{cos^2(x)}} \\ =5cos(x) ( -x^2tan^2(x) + x^2sec^2(x)+2xtan(x) ) \\ =5cos(x) ( -x^2*\frac{sin^2(x)}{cos^2(x)} + x^2*\frac{1}{cos^2(x)}+2x\frac{sin(x) }{cos(x)} ) \\ =5cos(x) ( -x^2*\frac{sin^2(x)}{cos^2(x)} + x^2*\frac{1}{cos^2(x)}+2x\frac{sin(x) }{cos(x)} ) \\ =5cos(x) ( x^2*\frac{1}{cos^2(x)} -x^2*\frac{sin^2(x)}{cos^2(x)}+2x\frac{sin(x) }{cos(x)} ) \\ =5cos(x) ( x^2[\frac{1}{cos^2(x)} -\frac{sin^2(x)}{cos^2(x)}]+2x\frac{sin(x) }{cos(x)} ) \\ =5cos(x) ( x^2*1+2x\frac{sin(x) }{cos(x)} ) \\ =5x^2cos(x) +10xsin(x) \\ When \;\;x=5 \qquad \text{is that radians or degrees?}\\ =125cos(5) +50sin(5) \\ \)

 Oct 6, 2016

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