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 Optimization Grading Rubric Derivative Calculator     at https://www.derivative-calculator.net/

PDF Files Limits connect-the-dots Derivatives connect-the-dots antiderivative Ch 5.1 notes.pdf Derivative &Antiderivative Cheat Sheets Calc Cheat Sheet -- derivatives, Trig and Hyperbolic Integrations, pdf format page 1 jpg   page 2 jpg   page 3 jpg   page 4 jpg   Sing the Derivatives Video

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 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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