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anonymous
 one year ago
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?
anonymous
 one year ago
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0First 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:\[\frac{ d }{ dx }(x^n)=n*x^{n1}\] 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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