The option (B) represents the derivative of y with respect to x option (B) is the correct choice.
What is differentiation?
The derivative of a function of a real variable in mathematics describes the sensitivity of the function value to a change in its argument.
We have:
[tex]\rm y= \dfrac{ln}{x^7}\right)[/tex]
To find the derivative of y with respect to x differentiate with respect to x.
[tex]= \rm \dfrac{d}{dx}\left(\dfrac{ln}{x^7}\right)[/tex]
Applying the divide rule:
[tex]\rm =\dfrac{\frac{d}{dx}\left(\ln \left(x\right)\right)x^7-\dfrac{d}{dx}\left(x^7\right)\ln \left(x\right)}{\left(x^7\right)^2}[/tex]
[tex]\rm =\dfrac{\dfrac{1}{x}x^7-7x^6\ln \left(x\right)}{\left(x^7\right)^2}[/tex]
[tex]\rm =\dfrac{1-7\ln \left(x\right)}{x^8}[/tex]
Thus, the option (B) represents the derivative of y with respect to x option (B) is the correct choice.
Learn more about the differentiation here:
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