Find the derivative of the function y left 3x 2... - SS3 Mathematics Differential Calculus (Differentiation) Question
Find the derivative of the function \(y = \left( 3x^{2} + 2 \right)^{2}\)
A
\(\6x\left( x^{2} + 3 \right)\)
B
12x
C
\(\ 3x^{2} + 2\)
D
\(\12x(3x^{2} + 2)\)
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Correct Option: D
Let \(u = 3x^{2} + 2\), \(\frac{du}{dx} = 6x\)
\(y = u^{2}\), \(\frac{dy}{du} = 2u\)
\[\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}\]
\[\frac{dy}{du} = 2u \times 6x = 2(3x^{2} + 2) \times 6x\]
\(= 12x(3x^{2} + 2)\)
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