Derivative of tangent
Builds on Tangent functionQuotient ruleDerivative of sineDerivative of cosinePythagorean trigonometric identity
Statement
The tangent function is differentiable at every with , and
Remarks
The quotient rule gives . The Pythagorean identity turns the numerator into .
The derivative is positive. So is strictly increasing on .
Mathlib states it as Real.hasDerivAt_tan.
Reading path
To understand this page from the ground up, read these 64 pages in order. The foundations come first.
- Limit point of a set definition
- Local maximum definition
- Sequence definition
- Limit of a function definition
- Local minimum definition
- Real sequence definition
- Subsequence definition
- Continuity at a point definition
- Derivative definition
- Bounded sequence definition
- Cauchy sequence definition
- Geometric sequence definition
- Limit of a sequence definition
- Monotone sequence definition
- Series definition
- Continuous function definition
- Differentiable function definition
- Fermat's theorem on stationary points statement
- Limit superior definition
- Cauchy sequences are bounded statement
- Sum of a finite geometric series statement
- Monotone convergence theorem for sequences statement
- Every sequence has a monotone subsequence statement
- Convergent sequence definition
- Pointwise convergence definition
- Squeeze theorem statement
- Partial sum definition
- Power series definition
- Differentiable functions are continuous statement
- Bolzano–Weierstrass theorem statement
- The sequence r^n tends to zero for |r| < 1 example
- Radius of convergence definition
- Convergent series definition
- Uniform convergence definition
- Sine and cosine definition
- Boundedness theorem statement
- Product rule statement
- Reciprocal rule statement
- Cauchy criterion for sequences statement
- Uniform convergence on a set definition
- Absolute convergence definition
- Tangent function definition
- A series of nonnegative terms converges iff its partial sums are bounded statement
- Series of functions definition
- Sum of a series definition
- Extreme value theorem statement
- Quotient rule statement
- Uniformly Cauchy sequence of functions definition
- Geometric series example
- Comparison test statement
- Rolle's theorem statement
- Root test statement
- Weierstrass M-test statement
- Mean value theorem statement
- Cauchy–Hadamard theorem statement
- Power series converge uniformly on smaller discs inside the radius of convergence statement
- A function with zero derivative is constant statement
- Uniform convergence of derivatives allows term-by-term differentiation statement
- Term-by-term differentiation statement
- Power series are differentiable inside the radius of convergence statement
- Derivative of cosine statement
- Derivative of sine statement
- Pythagorean trigonometric identity statement
- Derivative of tangent statement
Where this leads
2 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Differentiation_of_trigonometric_functions, From the quotient rule
About this page
| Tag | 0SAMR34WXC |
|---|---|
| URI | m2://0SAMR34WXC |
| Kind | statement, proposition |
| Writing | W0 stub |
| MSC | 33B10, 26A24 |
| Status | This copy of the site has no build data. Run m2 status 0SAMR34WXC. |
| Uses | Tangent function, Quotient rule, Derivative of sine, Derivative of cosine, Pythagorean trigonometric identity |
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