Cloned from: Calculus 1



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Derivative
Since the derivative is defined as the limit which finds the slope of the tangent line to a function, the derivative of a function at x is the instantaeous rate of change to the function at x.

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Find f' (x):

y = cos x
Ans:
f'(x) = -sin x
Find f' (x):

y = tan x
Ans:
f'(x) = sec2 x
Find f' (x):

y = sec x
Ans:
f'(x) = sec(x)tan(x)
Find f' (x):

y = csc x
Ans:
f'(x) = -csc(x)cot(x)

Find f' (x):

y = cot x
Ans:

f'(x) = -csc2(x)
d/dx(c) =

d/dx(c) = 0
d/dx(ax + b) =

d/dx(ax + b) = a
Power Rule:
If f(x) = x n , where n is any real number, then f'(x) = nx n-1 .
y = x 7 ,

then dy/dx =
.
dy/dx = 7x 6

Constant Multiple Rule:
d/dx cf(x) = c d/dx f(x)
y = 3x5, then dy/dx =
3 d/dx(x5) = 3(5x4)
= 15x4

Sum Rule
d/dx [ f(x) + g(x) ]
= d/dx f(x) + d/dx g(x)
Difference Rule

d/dx [ f(x) - g(x) ]
= d/dx f(x) - d/dx g(x)
Product Rule
d/dx [ f(x) • g(x) ]
= g(x) d/dx f(x) + f(x) d/dx g(x)
Quotient Rule
d/dx [ f(x) / g(x) ]
= [ g(x) d/dx f(x) - f(x) d/dx g(x) ] / [ g(x) ]2
Find f' (x):

y = sin x
f' (x) = cos x

Let f be a function, the derivative of f at x is given by:
sum of the angle formula
sin (a + b) = ???
sin (a + b) =
( cos a )( sin b ) + ( sin a )( cos b )
find the derivitive:
f(x) = -2x2 - 3x + 1 
f'(x) = -4x - 3
find the derivitive: 
f(x) = 3x/ 4
f'(x) = 9x / 4
f(x) = √x - 1  
f'(x) =
f'(x) = 1 / 2√x
f(x) = -√(x5)
f'(x) = 
f'(x) = - (5/2) x3/2
y = sinx
f'(x) =
f'(x) = cosx
f(x) = (3π) / 4
f' (x) = 
f' (x) = 0
Chain Rule
h(x) = f(g(x)) , h'(x) = f'(g(x)(g'(x))
f(x) = (x² + 1)5
f'(x) = ________
f' (x) = 5(x² + 1)4· 2x  
x of y cards