Solve 1/2/B^2

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

Differentiate w.r.t. B

$$-\frac{1}{B^{3}}$$

Steps Using Chain Rule

Express \frac{\frac{1}{2}}{B^{2}} as a single fraction.

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

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).

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

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}.

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

Simplify.

$$-4B^{1}\times \left(2B^{2}\right)^{-2}$$

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

$$-4B\times \left(2B^{2}\right)^{-2}$$

Evaluate

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

Solution Steps

Express \frac{\frac{1}{2}}{B^{2}} as a single fraction.

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