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  • Assertion: The derivative of the function  <img alt="f(x)=3 x^2+2 x \text { is } f^{\prime}(x)=6 x+2 ." src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%3D3%20x%5E2&plus;2%20x

Assertion: The derivative of the function  f(x)=3 x^2+2 x \text { is } f^{\prime}(x)=6 x+2 .

Reason: The derivative of a function is found by applying the power rule, which states that if  f(x)=a x^n, \text { then } f^{\prime}(x)=n a x^{(n-1)} .

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 function,  apply the power rule. Let's differentiate   f(x)=3 x^2+2 x term by term:

 

Differentiating the first term:\frac{d\left(3 x^2\right)}{d x}=3 * 2 x^{(2-1)}=6 x

 

Differentiating the second term:\frac{d(2 x)}{d x}=2 * 1 x^{(1-1)}=2

 

Therefore, the derivative off(x)=3 x^2+2 x \text { is } f^{\prime}(x)=6 x+2

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

 

 

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Anam Khan

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