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.

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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Using The Product Rule To Find The Derivative Of A Exponential Function

**Video Clip Length:** 1 minute 59 seconds

**Video Clip Views:** 28630

Using The Product Rule To Find The Derivative Of An Algebraic Complex Fractional Function

**Video Clip Length:** 5 minutes 59 seconds

**Video Clip Views:** 27243

Determining Points At Which Function Has Horizontal Tangent Line

**Video Clip Length:** 11 minutes 55 seconds

**Video Clip Views:** 19365

derivatives video clips for 12th grade math students.

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-16t^{2}. Find its instantaneous velocity after t seconds. Discuss the specialty about time t=15/8

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-16t

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...

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...

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)=x^{3}-6x^{2}+13x+15

and its total revenue function is

R(x) = 28...

(cost and profit) a one-product firm estimates that its daily total cost function (in suitable units) is

C(x)=x

and its total revenue function is

R(x) = 28...

derivatives homework help word problems for 12th grade math students.

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)= x^{3}/3 - 15x^{2} + 200x

C(x)= x

derivatives homework help questions for 12th grade math students.

I hope it will teach me the fundamentals for 11th grade and 12th grade Math.

I teach math to 9th grade -12th grade at a small city school in North Carolina. Knowing that each student in NC has to score levels 3 or 4 on the EOC Algebra 1 test to graduate, any real-life application type problems would be beneficial to the success of my students. Knowing also that matrces are heavily tested on the NC EOC test, this website appears that it would be helpful. Our textbooks do not offer many examples of matrices . Thank you.

It will help me understand derivatives much better.

finding derivatives of radical functions

I teach math to 9th grade -12th grade at a small city school in North Carolina. Knowing that each student in NC has to score levels 3 or 4 on the EOC Algebra 1 test to graduate, any real-life application type problems would be beneficial to the success of my students. Knowing also that matrces are heavily tested on the NC EOC test, this website appears that it would be helpful. Our textbooks do not offer many examples of matrices . Thank you.

It will help me understand derivatives much better.

finding derivatives of radical functions

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