Math · Calculus · Worked example

Differentiate (3x+1)²

Follow the inner and outer rates.

Separate the stages

Let u=3x+1 and y=u².

g^{'} (x) = 3, f^{'} (u) = 2 u

The outer rate is evaluated at u=3x+1.

f^{'} (g (x)) = 2 (3 x + 1)

Each unit of x causes three units of u.

\frac{d y}{d x} = 6 (3 x + 1)

The derivative is 18x+6.

Differentiate (2x−3)³.

Show the answer and explanation

The outer rate is 3u² at u=2x−3; multiply by the inner rate 2.

Change an input and predict the result before checking it.

Sources and scope

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