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Reference: Pearson Edexcel International A Level Pure Mathematics 3 Student Book. This chapter gives the rules for differentiating trig, exponential and logarithmic functions.
Main skills from this lesson
Memorise these until they feel automatic:
Use radians for calculus with trig functions.
The negative sign in d/dx(cos x) = -sin x is easy to lose.
Use the chain rule for a function inside a function.
If y = f(u) and u = g(x), then dy/dx = dy/du x du/dx.
Quick pattern: differentiate the outside, keep the inside, then multiply by the derivative of the inside.
d/dx [sin(3x)] = 3cos(3x)
Use the product rule for two multiplied functions:
If y = uv, then dy/dx = u(dv/dx) + v(du/dx).
Use the quotient rule for u/v. Keep your numerator bracketed so signs stay correct.
quotient numerator: v u' - u v'
If you can simplify before using quotient rule, simplify first.
Derivatives answer questions about change.
Study tip: write a short sentence after the calculation to explain what the derivative means.
Continue with quizzes, flashcards, or games when you are ready.