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Find dy/dx for y=5x^3-2x^2+7x-15

Step 1: To differentiate an equation there is a simple rule to follow. For y=axn dy/dx=anxn-1. so for an example y=x3, dy/dx=3x2. Therefore we just apply this rule into our equation.

Step 2: Break the equation down and do each factor of x seperately so 5x3 differentiates into 15x2, -2x2 differentiates to -4x, 7x differentiates to 7 and the 15 disappears from the end. This happens as the 15 just tells us where the line crosses the y axis and therefore has no bearing on the gradient.

Step 3: Put the differentiated parts back together to give the differentiated equation

dy/dx=15x2-4x+7

Matthew T. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor,...

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