APMA 1110 Test Review
Integration by parts - correct answer ✔✔∫ u dv = uv - ∫ v du
derivatives of sin, cos, and tangent (and sec) functions (6) - correct answer ✔✔d/dx sinx=cosx
d/dx cosx=-sinx
d/dx tanx=sec2x
d/dx sinu= cosu*u'
d/dx cosu= -sin(u)*u
'd/dx tanu = sec2u*u'
d/dx secx= secxtanx
derivatives of sec^2, cot, and csc functions - correct answer ✔✔d/dx sec^2x=tanx
d/dx -cotx= -csc^2x
d/dx -cscx= -cscxcotx
Derivative Rule for Inverses (arcsin, arccos, arctan) - correct answer ✔✔d/dx arcsinx = 1/rad(1-x^2)
d/dx arccosx = -(1/rad(1-x^2) )
d/dx arctan = 1/(1+x^2)
derivative of e and ln (4) - correct answer ✔✔d/dx e^x = e^x
d/dx e^f(x) = e^f(x) * f'(x)
d/dx lnx= 1/x
d/dx ln(f(x))= 1/f(x) * f'(x)
Anti-power rule - correct answer ✔✔(cx^n+1)/n+1
, Anti-chain rule substitution.
What things do you make the u? - correct answer ✔✔Make the u:
- something raised to a power
- something inside a trig function
- power of e
- denominator of a fraction
if the x doesn't cancel out when you are using a u substitution, what do you do? - correct answer
✔✔Take original u substitution and solve for x and plug x = in what hasn't been crossed out. Multiply u's
together and solve.
Antiderivative trig functions - correct answer ✔✔anti derivative of cosx: sinx
anti derivative of sinx: -cosx
anti derivative of -sinx: -cosx
anti derivative of sec^2x: tanx
anti derivative of secxtanx: secx
anti derivative of csc^2x: -cotx
anti derivative of tan^2x: tanx-x
anti derivative of tanx: ln|secx|
Antiderivative of e's and 1/x - correct answer ✔✔anti derivative of e is e
anti derivative of 1/x is ln|x|
Antiderivative of ln - correct answer ✔✔xlnx-x
antideriv of inverse sin - correct answer ✔✔xsin^-1x-∫x/(sqrt(1-x^2)
Choosing u - correct answer ✔✔Inverse
Log
Integration by parts - correct answer ✔✔∫ u dv = uv - ∫ v du
derivatives of sin, cos, and tangent (and sec) functions (6) - correct answer ✔✔d/dx sinx=cosx
d/dx cosx=-sinx
d/dx tanx=sec2x
d/dx sinu= cosu*u'
d/dx cosu= -sin(u)*u
'd/dx tanu = sec2u*u'
d/dx secx= secxtanx
derivatives of sec^2, cot, and csc functions - correct answer ✔✔d/dx sec^2x=tanx
d/dx -cotx= -csc^2x
d/dx -cscx= -cscxcotx
Derivative Rule for Inverses (arcsin, arccos, arctan) - correct answer ✔✔d/dx arcsinx = 1/rad(1-x^2)
d/dx arccosx = -(1/rad(1-x^2) )
d/dx arctan = 1/(1+x^2)
derivative of e and ln (4) - correct answer ✔✔d/dx e^x = e^x
d/dx e^f(x) = e^f(x) * f'(x)
d/dx lnx= 1/x
d/dx ln(f(x))= 1/f(x) * f'(x)
Anti-power rule - correct answer ✔✔(cx^n+1)/n+1
, Anti-chain rule substitution.
What things do you make the u? - correct answer ✔✔Make the u:
- something raised to a power
- something inside a trig function
- power of e
- denominator of a fraction
if the x doesn't cancel out when you are using a u substitution, what do you do? - correct answer
✔✔Take original u substitution and solve for x and plug x = in what hasn't been crossed out. Multiply u's
together and solve.
Antiderivative trig functions - correct answer ✔✔anti derivative of cosx: sinx
anti derivative of sinx: -cosx
anti derivative of -sinx: -cosx
anti derivative of sec^2x: tanx
anti derivative of secxtanx: secx
anti derivative of csc^2x: -cotx
anti derivative of tan^2x: tanx-x
anti derivative of tanx: ln|secx|
Antiderivative of e's and 1/x - correct answer ✔✔anti derivative of e is e
anti derivative of 1/x is ln|x|
Antiderivative of ln - correct answer ✔✔xlnx-x
antideriv of inverse sin - correct answer ✔✔xsin^-1x-∫x/(sqrt(1-x^2)
Choosing u - correct answer ✔✔Inverse
Log
