Calculus Integration and Derivatives Rules Flashcards
What is the constant rule
d/dx [c] = ?
Derivative of a constant is equal to zero.
Power Rule for Derivatives
d/dx [x^n] = nx^(n-1)
Product Rule for Derivative
d/dx [f(x)g(x)] = ?
f ‘ (x) g(x) + f(x) g’ (x)
Quotient Rule for Derivatives
d/dx [f(x)/g(x)] = ?
[g(x)f ‘(x) - f(x) g’ (x)] / [g(x)]^2
Exponential Rule for Derivative
d/dx b^x
b^x * d/dx (x)
Logarithmic Rule for Derivatives
d/dx ln (x)
1/x
Constant Multiple Rule for Derivatives
d/dx [c(f(x)] = ?
c f ‘ (x)
Sum Rule for Derivatives
d/dx [f(x) + g(x)] = ?
f ‘ (x) + g’ (x)
Difference Rule for Derivatives
d/dx [f(x) - g(x) ] = ?
f ‘ (x) - g’ (x)
Chain Rule for Derivatives
d/dx f(g(x)) = ?
f ‘ (g(x)) g’ (x)
d/dx (x) = ?
1
d/dx (sin x) = ?
cos x
d/dx (cos x) = ?
-sin x
d/dx (tan x) = ?
sec^2 (x)
d/dx (sec x) = ?
sec x tan x
d/dx (csc x) = ?
- csc x cot x
d/dx (cot x) = ?
-csc^2 (x)
d/dx (sin^-1 (x)) = ?
1/ sqrt (1-(x^2))
d/dx (cos^-1 (x)) = ?
-1/ sqrt (1-(x^2))
d/dx (tan^-1 (x)) = ?
1/sqrt (1 + x^2))
d/dx (a^x) = ?
a^x (ln a)
d/dx (e^x) = ?
e^x
d/dx log base a (x) = ?
1/x ln a
csc (tetha) = ?
1/sin (theta)
sec (tetha) = ?
1/ cos (tetha)
cot (tetha) = ?
1/ tan (theta)
Integration of a dx
ax + C
Power Rule for Integration
integration of x^n dx = [x^(n+1)]/n+1 + c, n not equal to -1.
Integration x^-1 dx
ln |x|+ c
Integration of e^x dx
e^x + c
Integration a^x dx
a^x/ln a + c
Integration kf(x) dx = ?
k integration f(x) dx.
Integration f(x) + g(x) dx = ?
Integration f(x) dx + Integration g(x) dx
Integration f(x) - g(x) dx = ?
Integration f(x) dx - Integration g(x) dx
Integration sin x dx
-cos x + c
Integration cos x dx
sin x + c
Integration sec^2 x dx = ?
tan x + c
Integration csc^2 x dx = ?
-cot x + c
Integration sec x tan x dx = ?
sec x + c
Integration csc x cot x dx = ?
-csc x + c
sin^2 x + cos^2 x = ?
1
sin^2 x = ?
1/2 [1- cos 2x]
cos^2 x = ?
1 - sin^2 x
sec^2 x = ?
1 + tan^2 x
csc^2 x = ?
1 + cot^2 x
cos^2 x = ?
1/2 [1 + cos 2x]
sin (2x) = ?
2 sin x cos x
