\( { \rm If} \ y = x^2 +7, { \rm \ differentiating} \ y \ {\rm with \ respect \ to} \ x\ {\rm gives}\)
\( x +7 \)
\( x +C , \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
\( 2x +7 \)
\( 2x \)
\(0.5 x^3 +C , \ {\rm where} \ C \ {\rm is \ an \ unknown \ constant.} \)
\( x = 3 \cos ( \pi t + \frac{2\pi}{3} ), \ {\rm find \ the \ value \ of } \frac{dx}{dt} {\rm when} \ t=1.0. \ Note \ the \ angle \ is \ measured \ in \ radians. \)
\( -0.86 \)
\( 8.2 \)
\( 0 \)
\( -2.6 \)
\( 1.5 \)
\( { \rm If} \ y = 6e^{2x} , { \rm \ differentiating} \ y \ {\rm with \ respect \ to} \ x\ {\rm gives}\)
\( 12e^{2x} \)
\( 6xe^2 \)
\( 6e^{2x} \)
\( 6xe^{2x} \)
\( 12e^x \)
\( { \rm If} \ y = 2{\rm sin}(2x+\pi), { \rm \ differentiating} \ y \ {\rm with \ respect \ to} \ x\ {\rm gives}\)
\( 4 {\rm cos}(2x+\pi) \)
\( 4x{\rm cos}(2x+\pi) \)
\( 4 {\rm sin}(2x+\pi) \)
\( 4x {\rm sin}(2x+\pi) \)
\( 2x {\rm cos}(2x+\pi) \)
\( { \rm An \ arrow \ is \ fired \ which \ travels \ with \ vertical \ motion \ described \ by } \ y = -5t^2+10t .\) \( { \rm \ It \ hits \ a \ target \ at \ t=1.5s. \ Is \ the \ arrow \ ascending, \ or \ descending \ when \ it \ hits?}\)
\( {\rm Ascending }\)
\( {\rm Descending }\)
