Asked by Francis
If Y = SecXTanX, find y" 4y' 4y.
I can easily do the second part of the question if I could if only I could find d first and second derivative of SecXTanX, pls do help.
I can easily do the second part of the question if I could if only I could find d first and second derivative of SecXTanX, pls do help.
Answers
Answered by
Reiny
well, finding y' and y'' is really the main part of the meal, the rest is just cleaning the dishes.
you should know the derivatives of the 6 basic trig functions by heart.
y' = secx(sec^2 x) + tanx(secxtanx) , by the product rule
= sec^3 x + tan^2 x secx
y'' = 3(sec^2 x)(secxtanx) + tan^2 x(secxtanx) + (secx)(2)(tanx)(sec^2 x)
= 3 sec^3 x tanx + secx tan^3 x + 2(sec^3 x)tanx
= 5sec^3 x tanx + secx tan^3 x
carry on
you should know the derivatives of the 6 basic trig functions by heart.
y' = secx(sec^2 x) + tanx(secxtanx) , by the product rule
= sec^3 x + tan^2 x secx
y'' = 3(sec^2 x)(secxtanx) + tan^2 x(secxtanx) + (secx)(2)(tanx)(sec^2 x)
= 3 sec^3 x tanx + secx tan^3 x + 2(sec^3 x)tanx
= 5sec^3 x tanx + secx tan^3 x
carry on
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