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Fiches sur les dérivés et les tangentes en math (terminale)

07/02/2022

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<h2 id="theoremofthelimitofthederivative">Theorem of the Limit of the Derivative</h2>
<p>This limit is called the derivative number. When a
<h2 id="theoremofthelimitofthederivative">Theorem of the Limit of the Derivative</h2>
<p>This limit is called the derivative number. When a

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.

Résumé - Maths

  • Theorems of the limit of the derivative explain the concept of derivative number at a given point
  • The formula for the tangent to a curve involves the slope at a specific point
  • Derivatives of usual functions can be found in a PDF, including exercises and examples
  • Graphing a tangent involves finding the equation at a specific abscissa point
  • Understanding derivatives is crucial for analyzing the rate of increase of a function and graphing tangents, and the "Derivative of Usual Functions" PDF is a valuable resource for mastering this concept.
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Anciennement en Terminale Math HGGSP (abandon de la spé physique en première), anglais et espagnol, avec option latin. J’espère que mes fiches pourront vous aider 🌻

Questions fréquemment posées sur Maths

Q: What is the limit called when a function f is derivable at a point a?

A: The 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.

Q: What is the formula for the tangent to a curve at the point A with an abscissa of a?

A: The tangent is called the line at the point A with a slope of f'(a): y = f'(a) (xx-a) + f(a)

Q: Where can a table of derivatives, limits, and theorems on usual functions be found?

A: A table of derivatives, limits, and theorems on usual functions can be found in the 'Derivative of Usual Functions' PDF.

Q: What is the equation of the tangent to the curve at the abscissa point 1?

A: The equation of the tangent to the curve at the abscissa point 1 can be found in the 'Derivative of Usual Functions' PDF.

Q: How can the rate of increase of a function and the tangent to a curve at a specific point be analyzed?

A: 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.

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