Solve A^2/BdivA^2/B

$$A ^ { 2 } / B \div A ^ { 2 } / B$$

Evaluate

$$\frac{1}{B^{2}}$$

Solution Steps

Express \frac{\frac{\frac{A^{2}}{B}}{A^{2}}}{B} as a single fraction.

$$\frac{\frac{A^{2}}{B}}{A^{2}B}$$

Express \frac{\frac{A^{2}}{B}}{A^{2}B} as a single fraction.

$$\frac{A^{2}}{BA^{2}B}$$

Cancel out A^{2} in both numerator and denominator.

$$\frac{1}{BB}$$

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

$$\frac{1}{B^{2}}$$

Differentiate w.r.t. B

$$-\frac{2}{B^{3}}$$

Steps Using Chain Rule

Express \frac{\frac{\frac{A^{2}}{B}}{A^{2}}}{B} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{\frac{A^{2}}{B}}{A^{2}B})$$

Express \frac{\frac{A^{2}}{B}}{A^{2}B} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{A^{2}}{BA^{2}B})$$

Cancel out A^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{1}{BB})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}B}(\frac{1}{B^{2}})$$

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(B^{2}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}B}(B^{2})$$

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}.

$$-\left(B^{2}\right)^{-2}\times 2B^{2-1}$$

Simplify.

$$-2B^{1}\left(B^{2}\right)^{-2}$$

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

$$-2B\left(B^{2}\right)^{-2}$$