## 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?

1. anonymous

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

2. anonymous

Thanks

3. anonymous

You are welcome.