derivative rules

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Last updated 1:38 PM on 11/6/25
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12 Terms

1
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d/dx [sin(x)]

\cos\left(x\right)

2
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d/dx [cos(x)]

-\sin\left(x\right)

3
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d/dx [tan(x)]

\sec^2\left(x\right)

4
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d/dx [csc(x)]

-\csc\left(x\right)\cot\left(x\right)

5
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d/dx [sec(x)]

\sec\left(x\right)\tan\left(x\right)

6
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d/dx [cot(x)]

-\csc^2\left(x\right)

7
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d/dx(sin-1(u))

\frac{u^{\prime}}{\sqrt{1-u^2}}

8
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d/dx(cos-1(u))

-\frac{u^{\prime}}{\sqrt{1-u^2}}

9
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d/dx(tan-1(u))

\frac{u^{\prime}}{1+u^2}

10
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d/dx(cot-1(u))

-\frac{u^{\prime}}{1+u^2}

11
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d/dx(sec-1(u))

\frac{u^{\prime}}{\left|u\right|\sqrt{u^2-1}}  

12
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d/dx(csc-1(u))

-\frac{u^{\prime}}{\left|u\right|\sqrt{u^2-1}}