Composite Rule to differentiate ?

Question

Use the Composite Rule to differentiate the function

    f(x)=(x^2-6x+23)^3/2

Answer 1

Recall that chain rule is:

dy/dx = dy/du * du/dx

Let:

u = x² - 6x + 32
du/dx = 2x - 6
y = u^(3/2)
dy/du = 3/2 u^(½)
==> 3√(u)/2

This yields:

f'(x) = 3√(u)/2 * (2x - 6)
==> 3√(x² - 6x + 32)/2 * 2(x - 3)
==> 3(x - 3)√(x² - 6x + 32)

I hope this helps!

Answer 2

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