CAIE IGCSE Additional Math 14.3 differentiate standard functions

Use this standard-derivatives page to apply known derivatives and chain-rule steps, then simplify dy/dx into the requested form.

Exam points

Differentiate powers, trig, exponential or logarithmic functions using the standard rules.
Use the chain rule on composite expressions such as (3x²+4)^(1/3) or tan²x.
Find first or second derivatives before substituting values such as x=0.

[Maximum number: 2]

It is given that $y=3\tan^2x$ for $0^\circ<x<360^\circ$ .

Show that $\frac{dy}{dx}=m\tan x\sec^2x$ , where m is an integer to be found.

$\frac{dy}{dx}=6\tan x\sec^2x$
B2; B1 for $\frac{d}{dx}(\tan^2x)=2\tan x\sec^2x$

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