Solve frac{xJ_{1}(x)}{J_{0}(x)}

$$\frac { x J _ { 1 } ( x ) } { J _ { 0 } ( x ) }$$

Evaluate

$$\frac{J_{1}x}{J_{0}}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{x^{2}J_{1}}{J_{0}x}$$

Cancel out x in both numerator and denominator.

$$\frac{J_{1}x}{J_{0}}$$

Differentiate w.r.t. x

$$\frac{J_{1}}{J_{0}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{J_{1}x}{J_{0}}x^{1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{J_{1}x}{J_{0}}x^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{J_{1}x}{J_{0}})$$

The derivative of a constant term is 0.

$$0$$