Question

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?

Answer 1

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:\[=-\frac{ 7 }{ x^2 }-\frac{ 1 }{ 7 }\]

Answer 2

Thanks

Answer 3

You are welcome.