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The equation of a curve is y = x^2 - 5x. Work out dy/dx

This is an example of differentiation. This can be useful in many concepts, one being finding the gradient of a line or curve at a certain point. To differentiate these types of equations, the rule is to multiply the front by the power and to take one from the power!

y = x^2 - 5x

We will take each part separately. Starting with x^2. We multiply the front (which is 1) by the power (which is 2), therefore the constant at the front is now 2. We take one from the power, so 2 - 1 = 1. Therefore the derivative of x^2 is 2x.

Next we take 5x. Multiply the front (5) by the power (1), and take 1 from the power (1 - 1 = 0). Therefore the derivative of 5x is 5.

Now, we put it all together! dy/dy = 2x - 5!

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