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42 Cards in this Set
- Front
- Back
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Finding a derivative by the limit process |
Limit. f (x+🔼x)-f (x) 🔼x->0 🔼x |
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f'(x) = |
m |
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f'(c) = |
Lim. f (x)-f (c) x->c. x-c |
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Power rule |
d/dx x^n=nx^n-1 |
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Constant multiple rule |
d/dx cf(x)=cf'(x) |
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a^-m |
1/a^m |
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Position function |
s(t)=-16t^2+Vot+So Vot: initial velocity So: initial height |
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Average velocity |
🔼s. Change in height 🔼t. Change in time |
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Instantaneous velocity |
v (t)=s'(t)=lim. s(t+🔼t)-s(t) 🔼t->0. 🔼t |
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Acceleration |
a (t)=v (t)=s"(t) |
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Speed |
lV'(t)l |
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Product rule |
d/dx f(x)*g(x)=f(x)g'(x)+g(x)f'(x) |
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Quotient rule |
Lowdeehigh-highdeelow Low^2 |
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d/dx tanx |
Sec^2x |
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d/dx cotx |
-csc^2x |
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d/dx secx |
secxtanx |
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d/dx cscx |
-cscxcotx |
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Trig identities |
Cos^2x+sin^2x=1 Sec^2x-tan^2x=1 Csc^2x-cot^2x=1 Cos2x=cos^2x-sin^2x Sin2x=2sinxcosx Tan2x= 2tanx/1-tan^2x |
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Chain rule |
1) dy/dx=dy/du*du/dx 2) dy/dx [f(g(x))]=f'(g(x))*g'(x) |
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d/dx sinu |
cosu*u' |
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d/dx cosu |
-sinu*u' |
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d/dx tanu |
Sec^2u*u' |
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d/dx cscu |
cscucotu*u' |
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d/dx secu |
Secutanu*u' |
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d/dx cotu |
-csc^2u*u' |
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d/dx e^u |
e^u*u' |
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ln(M)^p |
Pln(M) |
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ln(MN) |
ln(M)+ln(N) |
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ln(M/N) |
ln(M)-ln(N) |
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d/dx ln (x) |
1/x |
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d/dx ln(u) |
1/u * u' |
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d/dx a^x |
ln(a)*a^x |
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d/dx logaX |
1/ln(a)*x |
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d/dx logaU |
u'/ln(a)*u |
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Substitute y back in for |
Log differentiations |
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If looking for dy/dx at a point |
Solve for dy/dx and substitute that x,y value to solve |
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d/dx [arcsin u] |
u'/sq.rt.(1-u^2) |
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d/dx [arccos u] |
-u'/sq.rt.(1-u^2) |
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d/dx [arctan u] |
u'/1+u^2 |
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d/dx [arccot u] |
-u'/1+u^2 |
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d/dx [arcsec u] |
u'/lul sq.rt.(u^2-1) |
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d/dx [arccsc u] |
-u'/lul sq.rt.(u^2-1) |
