Theorem of the Limit of the Derivative
This limit is called the derivative number. When a has a finite limit in a: f(x)-f(a), f is derivable at a, with x being the abscissa point a.
Tangent to a Curve Formula
The tangent is called the line at the point A with a slope of f'(a):
y = f'(a) (xx-a) + f(a)
Derivative of Usual Functions
- f(x) = k₁ with RER, f'(x) = 0. Derivability on R
- f (x) = x on R, f'(x) = 1
- f (x) = xc^ awer 1 E IN sur TR, f'(x) = nc^"" sur R
- f(x)=√x on [0; +∞0 [₁ f (0) = 2√5 our ]0; +∞0 [ sur [R\ {0}, f'(d) = = = ² our R\ {0}
- f(x)= x² on R{0} with nEN, f'(c) == n² sur R\ {0}
- f(xx)= e² our RR, f'(x) = ex
- f(x) = u(x) + √(x)
- f(x) = cos x on R, f'(x) = -sinx on R
- f(x) = sin x on R, f'(c) = (as xc sur TR
- f(x) = tanx on J - Z ; = [₁ f'(x) = 1 + tan²³ x =
- f'(x)=√₁(x) + √'(xx)
- f(c) = Rx UGC) →> f'(x) = kx u²(x)
- f(x) = u(d) x v(x) = f'(x) = u²(x) * v (xx) + UGJ x v²(c)
Graphing a Tangent
The equation of the tangent to the curve at the abscissa point 1.
Derivative of Usual Functions PDF
A table of derivatives, limits and theorems can be found in the "Derivative of Usual Functions" PDF. This PDF includes exercises and corrected examples on derivative numbers, tangents, and equations.
Equation of the Tangent at a Point
The equation of the tangent to the curve at the point with an abscissa of 0: f is derivable at a, with x being the abscissa point a.
Conclusion
By understanding the derivative and the equation of the tangent, it's possible to analyze the rate of increase of a function and graph the tangent to a curve at a specific point. As the derivative is a fundamental concept in calculus, mastering it is essential in understanding the behavior of functions. The "Derivative of Usual Functions" PDF provides a comprehensive guide to help you understand and practice this crucial concept.
