Derivatives
In calculus, the derivative is a measurement of how a function changes when the values of its inputs change. Loosely speaking, a derivative can be thought of as how much a quantity is changing at some given point. For example, the derivative of the position or distance of a car at some point in time is the instantaneous velocity, or instantaneous speed (respectively), at which that car is traveling (conversely the integral of the velocity is the car's position).
A closely related notion is the differential of a function.
The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.
The process of finding a derivative is called differentiation. The fundamental theorem of calculus states that differentiation is the reverse process to integration.
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Top Derivatives Video Tutorials
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Determining Points At Which Function Has Horizontal Tangent Line
11 minutes 55 seconds
calculus, derivatives
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Differentiating A Trigonometric Function
57 seconds
calculus, derivatives, trigonometric functions, trigonometry
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Determining Points At Which Function Has Horizontal Tangent Line 2
3 minutes 26 seconds
calculus, derivatives
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Finding The Derivative Of A Rational Algebraic Fraction
4 minutes 27 seconds
calculus, derivatives
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Using The Product Rule To Find The Derivative Of An Algebraic Complex Fractional Function
5 minutes 59 seconds
algebra, algebraic fractions, calculus, complex fractions, derivatives, fractions, number sense, numbers, product rule
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Differentiating A Trigonometric Function 2
2 minutes 21 seconds
calculus, derivatives, trigonometric functions, trigonometry
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Using The Product Rule To Find The Derivative Of A Exponential Function
1 minute 59 seconds
calculus, derivatives, exponential functions, exponents, functions, number sense, product rule
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Using The Constant Multiple Rule To Find The Derivative Of A Rational Algebraic Fraction
2 minutes 8 seconds
algebra, algebraic fractions, calculus, constant multiple rule, derivatives, fractions, number sense, numbers
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Determining Points At Which Function Has Horizontal Tangent Line 4
2 minutes 9 seconds
calculus, derivatives
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Using The Constant Multiple Rule To Find The Derivative Of A Fractional Function
2 minutes 32 seconds
algebra, algebraic fractions, calculus, constant multiple rule, derivatives, fractions, number sense, numbers
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calculus, derivatives, trigonometric functions, trigonometry, algebra, algebraic fractions, complex fractions, fractions, number sense, numbers, product rule, exponential functions, exponents, functions, constant multiple rule, .
Top Derivatives Worksheets
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Top Derivatives Word Problems
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Problem 1:
Let f(t) be the weight (in grams) of a solid sitting in a beaker of water. Suppose that the solid dissolves in such a way that the rate of change (in grams/minute) of the wieght of the solid at any time t can be be determined from the weight using the formula:
f'(t)=-5(t)(2+f(t))
If there is 3 grams of solid at time t=2, estimate the amount of solid 1 second later.
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Derivatives Books
