# Basic Derivatives

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f(x) = x

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### 20 Terms

1

f(x) = x

dy/dx = 1

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2

f(x) = x^2

dy/dx = 2x

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3

f(x) = cos(x)

dy/dx = -sin(x)

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4

f(x) = sin(x)

dy/dx = cos(x)

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5

f(x) = tan(x)

dy/dx = sec^2(x)

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6

f(x) = csc(x)

dy/dx = -csc(x)cot(x)

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7

f(x) = sec(x)

dy/dx = sec(x)tan(x)

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8

f(x) = cot(x)

dy/dx = -csc^2(x)

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9

f(x) = x^3

dy/dx = 3x^2

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10

f(x) = x^4

dy/dx = 4x^3

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11

f(x) = e^x

dy/dx = e^x

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12

f(x) = e^(2x)

dy/dx = 2(e^(2x))

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13

f(x) = ln(x)

dy/dx = 1/x

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14

f(x) = ln(2x)

dy/dx = 2/x

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15

f(x) = log₁₀(x)

dy/dx = 1/((x)(ln(10))

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16

f(x) = 2^x

dy/dx = (2^x)(ln(2))

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17

f(x) = 2^(2x)

dy/dx = 2(2^x)(ln(2))

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18

Power Rule

dy/dx (x^n) = n(x^(n-1))

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19

Product Rule

dy/dx (f•g) = f • dy/dx(g) + g • dy/dx(f)

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20

Quotient Rule

dy/dx(f/g) = ((g)•d(f) - (f)d(g))/(g^2)

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