### 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/
 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) absement Sketchpad - absity, absement, displacement,velocity, acceleration, jolt, jounce, ... -- derivatives & antiderivatives of displacement absement definition - antiderivative of displacement, cumulative displacement nth derivatives of displacement - image 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 firsttimes the secondplusthe derivative of the secondtimes the first. the QUOTIENT OF TWO FUNCTIONS, a first divided by a second function, is the derivative of the firsttimes the secondminusthe derivative of the secondtimes the first,ALL divided bythe 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 ofthe derivative of the outerevaluated at the inner functionandthe derivative of the inner function.