## What are the derivatives of six trigonometric functions?

Table of Contents

The following table summarizes the derivatives of the six trigonometric functions, as well as their chain rule counterparts (that is, the sine, cosine, etc. of a function)….Derivatives of Trigonometric Functions.

Function | Derivative |
---|---|

arccosx = cos-1x | -1/√(1-x2) |

arctanx = tan-1x | 1/(1+x2) |

arccotx = cot-1x | -1/(1+x2) |

arcsecx = sec-1x | 1/(|x|∙√(x2-1)) |

## What is the derivative of the sine function?

For example, the derivative of the sine function is written sin′(a) = cos(a), meaning that the rate of change of sin(x) at a particular angle x = a is given by the cosine of that angle.

**How do you derive a function?**

Apply the power rule to differentiate a function. The power rule states that if f(x) = x^n or x raised to the power n, then f'(x) = nx^(n – 1) or x raised to the power (n – 1) and multiplied by n. For example, if f(x) = 5x, then f'(x) = 5x^(1 – 1) = 5.

**What are basic derivatives?**

The Derivative tells us the slope of a function at any point. There are rules we can follow to find many derivatives. For example: The slope of a constant value (like 3) is always 0. The slope of a line like 2x is 2, or 3x is 3 etc.

### Which are the six functions in trigonometry?

– ais the length of the side adjacent to the angle (x) in question. – ois the length of the side opposite the angle. – his the length of the hypotenuse.

### How do you take the derivative of a trig function?

– lim θ → 0 sinθ 6θ lim θ → 0 sin θ 6 θ – lim x → 0 sin(6x) x lim x → 0 sin ( 6 x) x – lim x → 0 x sin(7x) lim x → 0 x sin ( 7 x) – lim t → 0 sin(3t) sin(8t) lim t → 0 sin ( 3 t) sin ( 8 t) – lim x → 4 sin(x − 4) x − 4 lim x → 4 sin ( x − 4) x − 4 – lim z → 0 cos(2z) − 1 z lim z → 0 cos ( 2 z) − 1 z

**How to calculate a basic derivative of a function?**

– Find f ( x + h ). – Plug f ( x + h ), f ( x ), and h into the limit definition of a derivative. – Simplify the difference quotient. – Take the limit, as h approaches 0, of the simplified difference quotient.

**What are the basic trigonometric functions?**

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions. The basic trigonometric functions are sine, cosine, tangent, cotangent, secant and cosecant.