Asked by OMAR
FIND Y" if Y=ln(sec(x)+tan(x))
Answers
Answered by
Reiny
first simplify the inside
sec(x)+tan(x)
= (1 + sinx)/cosx
then y=ln(sec(x)+tan(x))
= ln((1 + sinx)/cosx)
= lin(1 + sinx) - ln(cosx)
y' = cosx/(1+sinx) - (-sinx)/cosx
= cosx/(1+sinx) + tanx
now differentiate this once more.
sec(x)+tan(x)
= (1 + sinx)/cosx
then y=ln(sec(x)+tan(x))
= ln((1 + sinx)/cosx)
= lin(1 + sinx) - ln(cosx)
y' = cosx/(1+sinx) - (-sinx)/cosx
= cosx/(1+sinx) + tanx
now differentiate this once more.
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