Differentiate $y = (3x + 5)^4$ with respect to $x$.
A$12(3x + 5)^3$CORRECT
B$4(3x + 5)^3$
C$3(3x + 5)^3$
D$12(3x + 5)^4$
GCEFurther MathematicsDifferentiation2023
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Why the answer is A, and why the others tempt you.
Using the chain rule: dy/dx = 4(3x + 5)³ × 3 = 12(3x + 5)³. Option B forgets to multiply by the derivative of the inner function (3), while C only uses the inner derivative without the power rule factor. Option D incorrectly keeps the original power.
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