Solve d/d^230000/40*3

$$d / d ^ { 2 } \frac { 30000 } { 40 } \times 3$$

Evaluate

$$\frac{2250}{d}$$

Solution Steps

Rewrite d^{2} as dd. Cancel out d in both numerator and denominator.

$$\frac{1}{d}\times \frac{30000}{40}\times 3$$

Divide 30000 by 40 to get 750.

$$\frac{1}{d}\times 750\times 3$$

Multiply 750 and 3 to get 2250.

$$\frac{1}{d}\times 2250$$

Express \frac{1}{d}\times 2250 as a single fraction.

$$\frac{2250}{d}$$

Differentiate w.r.t. d

$$-\frac{2250}{d^{2}}$$

Steps Using Definition of a Derivative

Rewrite d^{2} as dd. Cancel out d in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{d}\times \frac{30000}{40}\times 3)$$

Divide 30000 by 40 to get 750.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{d}\times 750\times 3)$$

Multiply 750 and 3 to get 2250.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{1}{d}\times 2250)$$

Express \frac{1}{d}\times 2250 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{2250}{d})$$

The derivative of ax^{n} is nax^{n-1}.

$$-2250d^{-1-1}$$

Subtract 1 from -1.

$$-2250d^{-2}$$