Derivatives


       
    Take a Derivative Using the
        Limit of the Difference Quotient
    Topics on this and other pages.
  • Calculus Pages
  • 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
  • fX.f'X.f''X.intX.gsp and Function Emojis
  • derivativeTests -- Derivative Tests & DerAnyFx
  • 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
  • DerivSin   -- full blown 4-page sketches ** Use this
  • DerSin   -- simple sine and tangent line. Use other DerivSin.
  • 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)
  • 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.


 


 
(Use the Chain Rule)
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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