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AP Calculus AB — Live

Nova

Speaking...

“Good — what's the derivative of 3x + 1?”

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AP Calculus AB — Voice SessionLIVE

14:32

Nova

Speaking...

“Good — you found the derivative of the outer function. Now what about the inner function? What's the derivative of 3x + 1?”

T

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QFind d/dx of f(x) = (3x + 1)&sup4;

Step 1 — Identify the chain rule

Let u = 3x + 1, so f(x) = u&sup4;

f'(x) = f'(u) · u'(x)

Step 2 — Differentiate outer

d/du [u&sup4;] = 4u³

Power rule: bring down the exponent

Step 3 — Differentiate inner

d/dx [3x + 1] = 3

Result

f'(x) = 4(3x + 1)³ · 3 = 12(3x + 1)³

Nova's Notes

Chain rule: differentiate the outer function, keep the inner, then multiply by the derivative of the inner function.