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Calculus Derivatives
d/dx(sinx)=
d/dx(uv)=
Calculus Derivatives
20 terms
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derivatives and derivative rules
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Questions
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Answers
1
d/dx(uv)=
u'+v'
du/dx(u)+dv/dx(v)
du/dx(v)+(u)dv/dx
u'v+uv'
2
d/dx(sinx)=
cosx
-cosx
cos
sin2x
3
d/dx(cscx)=
-csccotx
-cscxcotx
-cosxcotx
cscxcotx
4
d/dx(cos
-1
x)=
1/x2
-1/√(1-x2)
√(1-x2)
1/x2
5
d/dx(cotx)=
-csc2x
cscx
tanx
-secx
6
d/dx(csc
-1
x)=
lxlx2-1
lxl√(x2-1)
-1/x2-1
-1/lxl√(x2-1)
7
d/dx(tan
-1
x)=
1/(1+x2)
1+x2/x
1/1-x2
1+x2
8
d/dx(log
a
x)=
1/x lna
1/x
1/lna
x(lna)
9
d/dx(sec
-1
x)=
lxl/x2-1
1/(lxl√x2-1)
1/x(√x2-1)
-1/(lxl√x2-1)
10
d/dx (x
n
)=
n2xn-1
xn-1
nxn-1
nxn+1
11
d/dx(cosx)=
cos2x
sinx
-sinx
secx
12
d/dx(sin
-1
u)=
√1-u2
1/1-u2
1/√(1-u2)du/dx
-1/√(u2-1)(u)
13
d/dx(secx)
cot2x
-cotx
cscx
secxtanx
14
d/dx[f(u)]=
f(u)du/dx
f'(u)f(u)
(dy/du)(du/dx)
f'(u)du/dx
15
d/dx(cot
-1
x)=
-1/(1+x2)
-1+x2
1+x
1/x2
16
d/dx(e
u
)=
eu(du/dx)
eu(u)
e(du/dx)
ln u
17
d/dx(ln u)=
(1/u)
(1/u2)
(1/u) (du/dx)
(u/1) (dx/du)
18
d/dx(u/v)=
[du/dx(v)-(u)dv/dx]/v2
(u'v-uv')/v2
(u'v-uv')/u2
(du/dx-dv/dx)/v2
19
d/dx(a
x
)=
ax
lna
axlna
ax-1
20
d/dx(tanx)=
cscx
tan2x
sec2x
secx
