1.
fraction numerator 2 sin x cos x over denominator 1 plus 45 tan squared 15 x end fraction
2.
fraction numerator left parenthesis x plus tan cubed 15 x right parenthesis left parenthesis 2 sin x cos x right parenthesis minus left parenthesis 1 plus sin squared x right parenthesis left parenthesis 1 plus 45 tan squared 15 x s e c squared 15 x right parenthesis over denominator left parenthesis x plus tan cubed 15 x right parenthesis squared end fraction
3.
fraction numerator left parenthesis x plus tan cubed 15 x right parenthesis left parenthesis 2 sin x cos x right parenthesis minus left parenthesis 1 plus sin squared x right parenthesis left parenthesis 1 plus 45 tan squared 15 x right parenthesis over denominator left parenthesis x plus tan cubed 15 x right parenthesis squared end fraction
4.
fraction numerator 1 plus 2 sin x cos x over denominator 1 plus 15 tan squared 15 x end fraction
If f left parenthesis x right parenthesis equals square root of 1 plus 8 x end root
, find f space apostrophe left parenthesis a right parenthesis
for a equals 3
and the equation of the tangent line to f left parenthesis x right parenthesis
at x equals a
.
1.
f space apostrophe left parenthesis a right parenthesis equals 5 over 4
; equation of the tangent line is y equals fraction numerator 5 x minus 13 over denominator 4 end fraction
2.
f space apostrophe left parenthesis a right parenthesis equals negative 4 over 5
; equation of the tangent line is y equals fraction numerator negative 4 x plus 13 over denominator 5 end fraction
3.
f space apostrophe left parenthesis a right parenthesis equals 4 over 5
; equation of the tangent line is y equals fraction numerator 4 x plus 13 over denominator 5 end fraction
4.
f space apostrophe left parenthesis a right parenthesis equals negative 5 over 4
; equation of the tangent line is y equals fraction numerator negative 5 x minus 13 over denominator 4 end fraction