Algebra: Differentiation

The video tutorial covers differentiation, focusing on finding dy/dx for a given equation. It explains the rules of differentiation, including dropping the power and reducing it by one. The tutorial then moves on to solving for the range of x values where the curve has a negative gradient, using the quadratic formula. The process involves setting up an inequality and substituting values into the quadratic formula to find critical values. The video emphasizes careful substitution and understanding of differentiation rules to solve calculus problems effectively.

What is the process to find DY over DX for the equation y = X^3 - 2X^2 - 15X + 5?

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Explain the rules of differentiation that are applied when differentiating the term X^3.

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How do you differentiate the term -2X^2 and what is the resulting expression?

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What is the significance of the constant term (+5) when differentiating the function?

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Describe how to set up an inequality to find the range of values for X where the curve has a negative gradient.

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What are the critical values obtained from the quadratic formula for the equation derived from the differentiation?

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How can you express the range of values for X in inequality form based on the critical values found?

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