Derivatives: definition and basic rules | Khan Academy
The derivative of a function describes the function's instantaneous rate of change at a certain point. Another common interpretation is that the derivative gives us the slope of the line tangent to the function's graph at that point. Learn how we define the derivative using limits.
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Learn how to connect the graphs of a function, its first derivative, and its second derivative in this Khan Academy video.
Unit 2: Differentiation: definition and basic derivative rules
The derivative of a function describes the function's instantaneous rate of change at a certain point - it gives us the slope of the line tangent to the function's graph at that point. See how we define the derivative using limits, and learn to find derivatives quickly with the very useful power, product, and quotient rules.
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If the original graph is of a parabola, rather than a circle, then the graph of the derivative is a straight line, since d/dx [ax² + bx + c] = 2ax + b. If the original graph is a circle, then the graph of the derivative will be similar (but opposite) to the purple math image you linked to.
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The derivative & tangent line equations - Khan Academy
Discover how the derivative of a function reveals the slope of the tangent line at any point on the graph. We'll explore how to use this powerful tool to determine the equation of the tangent line, enhancing our understanding of instantaneous rates of change.
Derivative of 𝑒ˣ (video) | Khan Academy
Discover the fascinating property of the derivative of 𝑒ˣ, which remains 𝑒ˣ after differentiation. This unique characteristic is central to our understanding and exploration of exponential functions, showcasing the remarkable nature of the number 𝑒.
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Finding relative extrema (first derivative test) - Khan Academy
No, the derivatives approaching from either side of the maximum or minimum do not have to be symmetrical. Try graphing the function y = x^3 + 2x^2 + .2x. You have a local maximum and minimum in the interval x = -1 to x = about .25.
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Sal sketches a graph of f(x)=3x⁴-4x³+2 including extremum and inflection points.
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