If y = (3x - 1)^4, what is the numerical value of \frac{dy}{dx} evaluated at x = 1? — JAMB UTME

If $y = (3x - 1)^4$ , what is the numerical value of $\frac{dy}{dx}$ evaluated at $x = 1$ ?

Answer: 96

Applying the chain rule

\frac{d}{dx}[u^n] = n u^{n-1} \cdot \frac{du}{dx}

y = (3x - 1)^4

gives

\frac{dy}{dx} = 4(3x - 1)^3 \cdot 3 = 12(3x - 1)^3

. Evaluating this expression at

x = 1

yields

12(3(1) - 1)^3 = 12(2)^3 = 96

Differentiate

y = (3x - 1)^4

with respect to

x

using the chain rule.

\frac{dy}{dx} = 12(3x - 1)^3

Differentiate the outer power function to get

4(3x - 1)^3

and multiply by the derivative of the inner linear function

3x - 1

, which is 3.

Substitute

x = 1

into the derivative function.

Evaluating

12(3(1) - 1)^3

gives

12(2)^3 = 12 \times 8 = 96

Chain Rule of Differentiation

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