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Learn: Differentiation Basics
AQA 7357 A Level Mathematics
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Welcome!Today we'll explore differentiation, an essential part of calculus. It's all about understanding how things change. Let's dive in!
What is differentiation?Differentiation is the process of finding the derivative of a function. A derivative represents the rate of change of a quantity. For example, in physics, it can show how quickly an object's position changes over time.
Key idea: GradientThe derivative of a function at a point gives the gradient (slope) of the curve at that point. A steep gradient means rapid change, while a flat gradient means little change.
Quick check: What does a derivative represent?
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Rules of differentiationThere are key rules to help differentiate functions efficiently:Power Rule: For f(x) = xn, f'(x) = nxn-1.Constant Rule: The derivative of a constant is always 0.Sum Rule: Differentiate terms separately when added or subtracted.
Using the power rule, the derivative of x{{blank0}} is {{blank1}}x{{blank2}}.
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Real-world connectionImagine driving a car. The speedometer shows your speed, which is the derivative of your position (distance travelled) with respect to time. Faster changes in position mean higher speed!
Match the items on the left with their correct pairs on the right
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Review Time!You're doing great! Now let's test what you've learned about differentiation so far.
Which of the following are true about differentiation? (Select all that apply)
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Match the items on the left with their correct pairs on the right
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Well done!You've learned the basics of differentiation, including its importance, rules, and applications. Keep practising to build your confidence!
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