calculus

• Differentiating


  1. Find an expression that allows us to get the gradient at a point on a curve

  2. Find the gradient of the tangent to the point on a curve
• dy/dx


  Difference in y divided by the difference in x
• Differentiating x^2


  1. Multiply the coefficient by the power

  2. Reduce the power by 1
• For the graph y = x^2, the derivative is dy/dx = 2x
• Differentiating y = 3x^3 - 8x + 2

  1. Multiply the coefficient by the power for each term

  2. Reduce the power by 1 for each term
• Differentiating y = (3x - 2)(3x - 2)

  1. Expand the brackets first

  2. Then differentiate each term
• Differentiating y = 5x^2 - 3x + 7

  1. Multiply the coefficient by the power for each term

  2. Reduce the power by 1 for each term
• When x = 1, dy/dx = 10(1) - 3 = 7
• Differentiating x^3 + 4x^2 - 2

  1. Multiply the coefficient by the power for each term

  2. Reduce the power by 1 for each term
• Differentiating an expression


  1. Expand the top

  2. Simplify the expression into a single line

  3. Differentiate the simplified expression
• Root x


  Can be written as x^(1/2)