Basic Derivatives
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20 Terms
1
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f(x) = x
dy/dx = 1
2
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f(x) = x^2
dy/dx = 2x
3
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f(x) = cos(x)
dy/dx = -sin(x)
4
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f(x) = sin(x)
dy/dx = cos(x)
5
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f(x) = tan(x)
dy/dx = sec^2(x)
6
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f(x) = csc(x)
dy/dx = -csc(x)cot(x)
7
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f(x) = sec(x)
dy/dx = sec(x)tan(x)
8
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f(x) = cot(x)
dy/dx = -csc^2(x)
9
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f(x) = x^3
dy/dx = 3x^2
10
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f(x) = x^4
dy/dx = 4x^3
11
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f(x) = e^x
dy/dx = e^x
12
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f(x) = e^(2x)
dy/dx = 2(e^(2x))
13
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f(x) = ln(x)
dy/dx = 1/x
14
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f(x) = ln(2x)
dy/dx = 2/x
15
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f(x) = log₁₀(x)
dy/dx = 1/((x)(ln(10))
16
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f(x) = 2^x
dy/dx = (2^x)(ln(2))
17
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f(x) = 2^(2x)
dy/dx = 2(2^x)(ln(2))
18
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Power Rule
dy/dx (x^n) = n(x^(n-1))
19
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Product Rule
dy/dx (f•g) = f • dy/dx(g) + g • dy/dx(f)
20
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Quotient Rule
dy/dx(f/g) = ((g)•d(f) - (f)d(g))/(g^2)