7.1.5

Finding derivatives

Test yourself

Differentiation

The derivative of a function can be worked out through a process called differentiation.

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Differentiation

  • There are different ways to display the derivative of a function.
    • If your equation starts with y =, then the derivative of the equation is dydx\large\frac{dy}{dx}.
    • If your function starts with f(xx) =, then the derivative of the equation is f'(xx).
  • The exam may also ask you to find the rate of change, the gradient of the tangent or to differentiate a function.
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General rule

  • To differentiate a whole equation/function, each term should be differentiated individually.
  • The general rule for differentiating a term is:
    • f(xx) = axnax^n → f'(xx) = naxnax nn−1
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Examples

  • f(xx) = axnax^n → f'(xx) = naxnax nn−1
    • f(xx) = xx3 → f'(xx) = 3xx2
    • f(xx) = 2xx3 → f'(xx) = 6xx2
    • f(xx) = 6xx → f'(xx) = 6 (remember f(xx) = 6xx is the same as 6xx1)
    • f(xx) = 3xx4 → f'(xx) = 12xx3
    • f(xx) = 9 → f'(xx) = 0 (remember f(xx) = 9 is the same as 9xx0)
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Example 1 with multiple terms

  • For each term in an expression, use f(xx) = axnax^n → f'(xx) = naxnax nn−1
    • f(xx) = xx3 + 2xx2 + 7xx
    • f'(xx) = 3xx2 + 4xx + 7
Illustrative background for Example 1 with multiple termsIllustrative background for Example 1 with multiple terms ?? "content

Example 1 with multiple terms

  • For each term in an expression, use f(xx) = axnax^n → f'(xx) = naxnax nn−1
    • f(xx) = 3xx4 + 5xx3 + 4xx2
    • f'(xx) = 12xx3 + 15xx2 + 8xx

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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