Derivatives


    Topics on this and other pages.
  • Calculus Pages
  • Take a Derivative by Substitution
  • Implicit Differentiation
  • Sine & Cosine
  • Derivatives in Words & Symbols
Derivative Calculator
    at https://www.derivative-calculator.net/
sketchpad sketchpad
Visit the Interactive Sketch Pad Material
On Derivatives
    Limits
  • limh4Dx   -- Really shows the derivative is the limit of the diference quotient. Use this one!!
    Derivatives
  • DerAnyFx -- Derivative of Any Function
        * One may trace the function and see coordinates displayed.
        * One may edit the function.
        * One may graph the approximate derivative function.
          1 - f(x) w/tangent line
          2 - f(x) & TRACE
          3 - any f(x): x, f(x), f'(x), f''(x)
          4 - sin(x): x, f(x), f'(x), f''(x)
  • DerCos -- Derivative of Cosine
  • Dere2x -- Derivative of the exponential
  • Derlnx -- Derivative of the Natural Log
  • DerReciprocal -- Derivative of the Reciprocal Function
  • DerSqrt -- Derivative of the Square Root
  • DerReciprocal   -- by use of a tangent line
  • DERe2x   -- by use of a tangent line
  • DerSqrt   -- simple curve and tangent. Could make it fancy.
  • DerSquare   -- simple graph w/tangent of x2. Could make it fancy.
    Trig Derivatives
  • DerCos   -- cosine graph, movable tangent line w/equation,
        * m derived by simple m formula (h=.01),
        * "derivative" may be graphed.
  • DerivCos   -- display cosine graph and entire difference quotient triangle (not the best)
  • DerivSin   -- full blown 4-page sketches ** Use this
  • DerSin   -- simple sine and tangent line. Use other DerivSin.
  • DerTan   -- tangent function & tangent line graphed, actual derivative function is provided & may be graphed.

The derivative of:

  a CONSTANT
is
zero.

  the PRODUCT OF A CONSTANT AND A FUNCTION
is
the product of the constant and the derivative of the function.

  the PRODUCT OF TWO FUNCTIONS, a first and a second function,
is
the derivative of the first
times the second
plus
the derivative of the second
times the first.

  the QUOTIENT OF TWO FUNCTIONS, a first divided by a second function,
is
the derivative of the first
times the second
minus
the derivative of the second
times the first,
ALL
divided by
the square of the second.


 


 
a COMPOSITE FUNCTION, a FUNCTION OF A FUNCTION,
a function and its argument a function, an outer function and the inner function,
is
the product of
the derivative of the outer
evaluated at the inner function
and
the derivative of the inner function.





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