Derivatives
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Last updated 6:29 PM on 12/9/22
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23 Terms
1
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Definition of Derivative
lim h->0 f(x+h)-f(x)/h
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Product Rule
(f*g)'(x) =
f(x)*g'(x) + g(x)*f'(x)
f(x)*g'(x) + g(x)*f'(x)
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Quotient Rule
(f/g)'(x) =
g(x)*f'(x) - f(x)*g'(x) / [g(x)]^2
g(x)*f'(x) - f(x)*g'(x) / [g(x)]^2
![(f/g)'(x) =
g(x)*f'(x) - f(x)*g'(x) / [g(x)]^2](https://knowt-user-attachments.s3.amazonaws.com/2bd0a68b9a7a40cc8299260cedfda4db.jpg)
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d/dx cos(x)
-sin(x)
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d/dx sin(x)
cos(x)
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d/dx e^x
e^x
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d/dx ln(x)
1/x
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d/dx a^x
(a^x) ln(a)
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d/dx loga (x)
1/(x ln a)
10
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d/dx sin(x)
cos(x)
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d/dx cos(x)
-sin(x)
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d/dx tan(x)
sec^2(x)
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d/dx cot(x)
-csc^2(x)
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d/dx sec(x)
sec(x)*tan(x)
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d/dx csc(x)
-csc(x)*cot(x)
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Chain Rule
d/dx f(g(x)) = f'(g(x))*g'(x)
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Inverse Functions
d/dx (f^-1 (x)) = 1/f'(f^-1 (x))
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d/dx sin^-1 (x)
d/dx arcsin(x)
d/dx arcsin(x)
1/sqrt(1-x^2)
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d/dx cos^-1 (x)
d/dx arccos(x)
d/dx arccos(x)
-1/sqrt(1-x^2)
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d/dx sec^-1 (x)
d/dx arcsec(x)
d/dx arcsec(x)
1/|x|*sqrt(x^2-1)
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d/dx csc^-1 (x)
d/dx arccsc(x)
d/dx arccsc(x)
-1/|x|*sqrt(x^2-1)
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d/dx tan^-1 (x)
d/dx arctan(x)
d/dx arctan(x)
1/x^2+1
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d/dx cot^-1 (x)
d/dx arccot(x)
d/dx arccot(x)
-1/x^2+1
