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Calculating Derivative from First Principles - WJEC C1 Past Paper Question

Learn how to differentiate algebraic expressions using first principles. This method involves finding the gradient of the tangent to a curve. Follow the step-by-step workings provided to understand the process thoroughly. This explanation is from a WJEC C1 past paper question.

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Calculating Derivative from First Principles - WJEC C1 Past Paper Question

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  1. DIFFERENTIATION FROM FIRST PRINCIPLES WJEC C1 PAST PAPER QUESTION January 2008

  2. Given that Find From first Principles Remember that this is the DERIVATIVE. We are asked to DIFFERENTIATEusing FIRST PRINCIPLES REMEMBER that the DERIVATIVE means the GRADIENT OF THE TANGENT to a curve. Here we will end up with an algebraic expression because we do not know the specific point to find the gradient.

  3. To obtain we substitute Wherever we see the x in the function The formula that we will use is This is our function that we wish to differentiate

  4. Expand brackets and simplify WORKINGS This will be the SAME in EVERY Case!!! EXPAND BRACKETS This can NOT simplify so DON’T EVEN TRY!!!

  5. The numerator left will ALWAYS have a common factor of You can ALWAYS cancel Consider the gradient of the chord The WHOLE of the first bracket will ALWAYS cancel out with parts of the second bracket So this is the gradient of the chord

  6. Gets closer and closer to ZERO So now we take the LIMIT as TO CONCLUDE

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