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All derivatives of circular trigonometric functions can be found from those of sin(x) and cos(x) by means of the quotient rule applied to functions such as tan(x) = sin(x)/cos(x). Knowing these derivatives, the derivatives of the inverse trigonometric functions are found using implicit differentiation.
The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.
In trigonometry, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined.
In other words, the function sine is differentiable at 0, and its derivative is 1. Proof: From the previous inequalities, we have, for small angles sin θ < θ < tan θ {\displaystyle \sin \theta <\theta <\tan \theta } ,
Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
In calculus, the quotient rule is a method of finding the derivative of a function that is the ratio of two differentiable functions. Let () = (), where both f and g are differentiable and ()
Second-order Taylor series approximation (in orange) of a function f (x,y) = e x ln(1 + y) around the origin. In order to compute a second-order Taylor series expansion around point (a, b) = (0, 0) of the function (,) = (+), one first computes all the necessary partial derivatives:
The derivative of ′ is the second derivative, denoted as ″ , and the derivative of ″ is the third derivative, denoted as ‴ . By continuing this process, if it exists, the n {\displaystyle n} th derivative is the derivative of the ( n − 1 ) {\displaystyle (n-1)} th derivative or the derivative of order ...