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Calculus I Essentials

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6. Derivatives
A lesson with Krista King Math

Learn how to answer one of the most important questions in calculus by calculating the rate of change of a function at a point (aka taking the derivative)!

Learn how to answer one of the most important questions in calculus by calculating the rate of change of a function at a point (aka taking the derivative)!

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2 CQ
7. Definition of the Derivative | Example
A lesson with Krista King Math

Understand derivatives with help from this lesson on difference quotients. See how to plug in values and functions and then simplify confusing equations.

Understand derivatives with help from this lesson on difference quotients. See how to plug in values and functions and then simplify confusing equations.

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9 CQ
8. Equation of the Tangent Line | Example
A lesson with Krista King Math

In this lesson from IntegralCalc, brush up on your calculus skills and work through a problem to find the equation of a line tangent to a particular function!

In this lesson from IntegralCalc, brush up on your calculus skills and work through a problem to find the equation of a line tangent to a particular function!

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5 CQ
9. Implicit Differentiation | Example
A lesson with Krista King Math

Don’t be intimidated by long implicit differentiation problems! Learn how to solve this type of equation with help from Krista, founder of IntegralCalc.

Don’t be intimidated by long implicit differentiation problems! Learn how to solve this type of equation with help from Krista, founder of IntegralCalc.

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5 CQ
10. Optimization
A lesson with Krista King Math

Learn how to solve optimization problems and find the extremes, the local or global minima or maxima of a function, in this lesson from integralCALC.

Learn how to solve optimization problems and find the extremes, the local or global minima or maxima of a function, in this lesson from integralCALC.

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Nooloo W
What exactly does she mean when she says that as h goes to 0 we get the slope?
Krista King Math
Hey Nooloo, The idea is that as you make the value of h smaller and smaller and smaller, eventually it gets "infinitely small," until the value of h is as close to 0 as possible. At that point, you get the derivative of the function at that point. Since the derivative is the slope, taking h closer and closer to 0 means you're finding the slope of the function at that point.
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Susan S
it seems that in your calculating a derivative of y=x/(1-2x) you had the math right until you simplified. Should be: f'(x) = 1/(1-2x)^2 = 1/(4x^2-4x+1) not: 4x^2-4x+1 Otherwise you do an excellent straight forward easy to follow job!
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Martha P
This was great! Showing step by step was really helpful.
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Ken G
For vectors a? and b? , both of the same dimensions and based at the same point, show that they satisfy ||a+b|| 2 +2||a+b|| = 2||a||2+2||b|| 2 Note: you must prove this identity without using components; use only vector notation and vector operations! Calculate dist(Q,?) where, Q(2,1,1), and ? is determined by the normal vector to the plane n? =(2,6,9)P and the point P(8,?3,1) lies on the plane.
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Carol J
Thank you
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