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Rules of Derivative
22 Rules of Derivatives
23
Mathematics
Undergraduate 2
05/28/2015
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Term
Constant Rule
 Definition
y=c
dy/dx=0
Term
Power Rule
 Definition
y=x^n
dy/dx=nx^n-1
Term
Constant Multiple Rule
 Definition
y=cx^n
dy/dx=ncx^n-1
Term
Sum Rule
 Definition
y=f(x)+g(x)
dy/dx=f'(x)+g'(x)
Term
Difference Rule
 Definition
y=f(x)-g(x)
dy/dx=f'(x)-g'(x)
Term
Product Rule
 Definition
y=f(x)*g(x)
dy/dx=f'(x)g(x)+f(x)g'(x)
Term
Quotient Rule
 Definition
y=f(x)/g(x)
dy/dx=g(x)f'(x)-f(x)g'(x)/(g(x))^2
Term
Exponent Rule
 Definition
y=e^x
dy/dx=e^x
Term
Exponent Rule (a)
 Definition
y=e^ax
dy/dx=ae^ax
Term
Sine Function Rule
 Definition
y=sinx
dy/dx=cosx
Term
Cosine Function Rule
 Definition
y=cosx
dy/dx=-sinx
Term
Tangent Function Rule
 Definition
y=tanx
dy/dx=sec^2(x)
Term
Cosecant Function Rule
 Definition
y=cscx
dy/dx=-cscxcotX
Term
Secant Function Rule
 Definition
y=secx
dy/dx=tanxsecx
Term
Cotangent Function Rule
 Definition
y=cotx
dy/dx=-csc^2(x)
Term
Chain Rule
 Definition
Term
Exponential Rule
 Definition
y=e^x
Term
Non-"e" Exponential Rule
 Definition
y=a^x
dy/dx=(a^x)ln a
Term
Natural Log Rule
 Definition
y=ln x
dy/dx=1/x
Term
Log Rule
 Definition
y=LogbX
dy/dx= 1/xlnb
Term
Inverse Sine Rule
 Definition
y=sin^-1(x) dy/dx=1/(1-x^2)^1/2
Term
Inverse Tangent Rule
 Definition
y=tan^-1(x) dy/dx=1/(x^2)+1
Term
Inverse Secant Rule
 Definition
y=sec^-1(x) dy/dx=1/|x|((x^2)-1)^1/2
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