Solve d(Ax+b/x)/dx

$$\frac { d ( A x + \frac { b } { x } ) } { d x }$$

Evaluate

$$A-\frac{b}{x^{2}}$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$Ax^{1-1}-bx^{-1-1}$$

Subtract 1 from 1.

$$Ax^{0}-bx^{-1-1}$$

Multiply -1 times b.

$$Ax^{0}+\left(-b\right)x^{-1-1}$$

Subtract 1 from -1.

$$Ax^{0}+\left(-b\right)x^{-2}$$

For any term t except 0, t^{0}=1.

$$A\times 1+\left(-b\right)x^{-2}$$

For any term t, t\times 1=t and 1t=t.

$$A+\left(-b\right)x^{-2}$$

Differentiate w.r.t. x

$$\frac{2b}{x^{3}}$$