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Year 11 · Calculus
Chain, product and exponential derivatives
Beyond the power rule: chain rule for a function inside a function, product rule for two multiplied, and standard derivatives of eˣ, sin, cos, ln.
How to do it
- Chain: derivative of the outside times derivative of the inside.
- Product: u′v + uv′.
- d/dx eᵏˣ = k eᵏˣ, d/dx sin kx = k cos kx, d/dx ln u = u′/u.
Worked example
Differentiate y = ln(2x − 3)
d/dx ln(u) = u′/u with u = 2x − 3, u′ = 2: 2/(2x − 3).
Answer: 2/(2x − 3)
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Watch outDo not forget to multiply by the derivative of the inside.
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