Mathematics (AS)·Differentiation · NSSCAS 2.4.1
Differentiating eˣ, ln x & trig functions
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In this lesson you will learn the five standard derivatives you must know by heart: eˣ, ln x, sin x, cos x and tan x. You will use them term by term on sums and differences, then bring back the chain rule to differentiate composites like e^(2x), ln(3x+1) and sin(3x). By the end you will evaluate a real gradient and find the equation of a tangent line, all at AS standard.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 2.4.1):
- Use the derivatives of eˣ, ln x, sin x, cos x and tan x, together with constant multiples, sums and differences.
- Differentiate composite functions built from eˣ, ln x and the trig functions using the chain rule.
- Apply these derivatives to evaluate a gradient at a point and to find the equation of a tangent line.
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