Calculus 1_Test 3 Memorization

d/dx(e^u)

e^u*u’

d/dx(a^u)

a^u*ln(a)*u’

d/dx(ln x)

1/x

d/dx(ln u)

u’/u

d/dx(logaU)

u’/u ln a

y=sin^-1(x)

x=sin(y)

Domain restriction for y=sin^-1(x)

[-π/2 , π/2 ]

y=cos^-1(x)

x=cos(y)

Domain restriction for y=cos^-1(x)

[0,π ]

y=tan^-1(x)

x=tan(y)

Domain restrictions for y=tan^-1(x)

(-π/2 , π/2 )

y=cot^-1(x)

x=cot(y)

Domain restrictions for y=cot^-1(x)

(0,π )

y=csc^-1(x)

x=csc(y)

Domain Restrictions for y=csc^-1(x)

[π/2 , 0) U (0, π/2 ]

y=sec^-1(x)

x=sec(y)

Domain Restrictions for y=sec^-1(x)

[0,π/2 ) U (π/2 , π ]

sin²(a) + cos² (a) =

1

tan²(a) + 1 =

sec²(a)

cot² + 1 =

csc² (a)

d/dx (arcsin(x))

1/√1-x²

d/dx (arctan(x))

1/1+x²

d/dx(arcsec(x))

1/IxI √x²-1

d/dx[arccos(x)]

-1/√1-x²

d/dx[arccot(x)]

-1/1+x²

d/dx[arcsec(x)]

-1/IxI √x²-1

sinh(x)=

e^x-e^-x/2

cosh(x)=

e^x+e^-x/2

tanh(x)=

sinh(x)/cosh(x)

sech(x)

1/cosh(x)

coth(x)=

1/tanh(x)

csch(x)=

1/sinh(x)

cosh²(x)-sinh²(x)=

1

cosh(x)+sinh(x)=

e^x

cosh(x)-sinh(x)=

e^-x

d/dx [sinh(x)]=

cosh(x)

d/dx [cosh(x)]=

sinh(x)

d/dx [sech(x)]=

-sech(x)tanh(x)

d/dx [tanh(x)]=

sech²(x)

d/dx [csch(x)] =

-csch(x)coth(x)

d/dx [coth(x)]=

-csch²(x)