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  • Assertion: The derivative of the composite function   is<i

Assertion: The derivative of the composite function  g(x)=(2x+1)^{3} isg^{\prime}(x)=6(2 x+1)^2

Reason: When differentiating a composite function, apply the chain rule, which states that if  h(x)=f(g(x)) \text {, then } h^{\prime}(x)=f^{\prime}(g(x))^* g^{\prime}(x) \text {. }

Option: 1

Both assertion and reason are true, and the reason is a correct explanation of the assertion.

 

 


Option: 2

Both assertion and reason are true, but the reason is NOT a correct explanation of the assertion.

 


Option: 3

The assertion is true, but the reason is false.

 


Option: 4

The assertion is false, but the reason is true.


Answers (1)

best_answer

To find the derivative of the given composite function,  apply the chain rule. Let's differentiate  g(x)=(2x+1)^{3}   step by step:

Let's define f(u)=u_{\text {and }}^3 g(x)=2 x+1 \text {, where } u=2 x+1

Differentiatingf(u): f^{\prime}(u)=3 u^{(3-1)}=3 u^2

Differentiating g(x): g^{\prime}(x)=2

Applying the chain rule: g^{\prime}(x)=f^{\prime}(g(x)) * g^{\prime}(x)=3(2 x+1)^2 * 2

Simplifying the expression: g^{\prime}(x)=6(2 x+1)^2

Therefore, the derivative of g(x)=(2 x+1)^3 \text { is } g^{\prime}(x)=6(2 x+1)^2

In this case, the assertion is true, and the reason correctly explains how to obtain the derivative of a composite function using the chain rule.

 

 

Posted by

Divya Prakash Singh

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