Calculus: Derivatives Help

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Calculus: 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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Calculus: Derivatives Videos

Using The Product Rule To Find The Derivative Of A Exponential Function
Video Clip Length: 1 minute 59 seconds
Video Clip Views: 34012

derivatives, exponential functions, exponents, functions, product rule
Using The Product Rule To Find The Derivative Of An Algebraic Complex Fractional Function
Video Clip Length: 5 minutes 59 seconds
Video Clip Views: 30639

algebraic fractions, complex fractions, derivatives, fractions, number sense, numbers, product rule
Determining Points At Which Function Has Horizontal Tangent Line
Video Clip Length: 11 minutes 55 seconds
Video Clip Views: 21338

derivatives, tangent line
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Calculus: Derivatives Word Problems

A ball is thrown vertically upwards with an initial velocity
A ball is thrown vertically upwards with an initial velocity of 60m/s. After time t seconds, its height above the ground is given as s=60t-16t2. Find its instantaneous velocity after t seconds. Discuss the specialty about time t=15/8
A one-product firm estimates
(cost and profit) a one-product firm estimates that its daily total cost function (in suitable units) is
C(x)=x3-6x2+13x+15
and its total revenue function is
R(x) = 28...
Let f(t) be the weight (in grams) of a solid
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...
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Calculus: Derivatives Practice Questions

Find the point on the curve y-axis which is nearest the point (4,0)
Find the marginal cost function, average cost function, and marginal average cost function for the total cost function of:
C(x)= x3/3 - 15x2 + 200x

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