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14 Cards in this Set
- Front
- Back
- 3rd side (hint)
Derivative of a constant times a function
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D(c f(x) ) / d(x) = C • f'(x)
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Derivative of a constant
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Always zero
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Derivative of a power
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d(x^n) / d(x) = n(X)^ n-1
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Derivative of the sum/difference of 2 functions
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d( f(x) + g(x) ) / d(x) = f'(x) + g'(x)
d( f(x) - g(x) ) / d(x) = f'(x) - g'(x) |
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Product rule
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d( f o g) (x) / d(x) =
f(x)•g'(x) + g(x)•f'(x) = 1st • derivative of 2nd + 2nd • derivative of 1st |
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Quotient rule
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d( f/g) (x) / d(x) =
g(x) • f'(x) - f(x) • g'(x) \ (g(x))^2 Bottom•derivative of top - top•derivative of bottom / bottom^2 |
B•T' - T•B' / B^2
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Derivative of sine
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d(sin x) / dx = cos x
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Derivative of cosine
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d(cos x) / dx = -sin x
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Name starts with c - derivative is negative
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Derivative of tangent
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d(tan x) / dx = sec ^2 x
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Derivative of secant
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d(sec x) / dx = sec x tan x
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Derivative of cosecant
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d(csc x) / dx = -csc x cot x
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Name starts with c - derivative is negative
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Derivative of cotangent
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d(cot x) / dx = -csc ^2 x
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Name starts with c - derivative is negative
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Chain rule
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h(x) = f (g(x)) =
h'(x) = f' ( g(x) ) • g'(x) •Derivative of outside function •evaluated at the inside function in parenthesis •multiplied by derivative of inside function |
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Definition of derivative
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lim ( f(w) - f(x) / w-x )
w->x lim ( f(x+h) - f(x) / h ) h->0 |
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