I am asked to find the derivative: y=7/x - x/7 I am given four choices. A) dy/dx= -7/x^2 - 1/7 B) dy/dx= -7x -1/7 C) dy/dx= 7/x^2 - 1/7 D) dy/dx= -7/x^2 + x/7 narrowing them down I am left with A or C as -7/x^2 I believe is correct, but why isn't the second half +x/49 or 1/49?

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I am asked to find the derivative: y=7/x - x/7 I am given four choices. A) dy/dx= -7/x^2 - 1/7 B) dy/dx= -7x -1/7 C) dy/dx= 7/x^2 - 1/7 D) dy/dx= -7/x^2 + x/7 narrowing them down I am left with A or C as -7/x^2 I believe is correct, but why isn't the second half +x/49 or 1/49?

Calculus1
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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First differentiate the sum term by term and factor out constants: \[=7(\frac{ d }{ dx }(\frac{ 1 }{ x }))-\frac{ 1 }{ 7 }(\frac{ d }{ dx }(x))\] Now you use the power rule:\[\frac{ d }{ dx }(x^n)=n*x^{n-1}\] which gives you:\[=-\frac{ 1 }{ 7 }(\frac{ d }{ dx }(x))+7*\frac{ -1 }{ x^2 }\] now you can simplify that:\[=-\frac{ 7 }{ x^2 }-\frac{ 1 }{ 7 }(\frac{ d }{ dx }(x))\] and the derivative of x is 1:\[=-\frac{ 7 }{ x^2 }-\frac{ 1 }{ 7 }\]
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