Solve 160*1000/16*p=

$$160 * 1000 / 16 * p =$$

Evaluate

$$10000p$$

Solution Steps

Reduce the fraction \frac{1000}{16} to lowest terms by extracting and canceling out 8.

$$160\times \frac{125}{2}p$$

Express 160\times \frac{125}{2} as a single fraction.

$$\frac{160\times 125}{2}p$$

Multiply 160 and 125 to get 20000.

$$\frac{20000}{2}p$$

Divide 20000 by 2 to get 10000.

$$10000p$$

Differentiate w.r.t. p

$$10000$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{1000}{16} to lowest terms by extracting and canceling out 8.

$$\frac{\mathrm{d}}{\mathrm{d}p}(160\times \frac{125}{2}p)$$

Express 160\times \frac{125}{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{160\times 125}{2}p)$$

Multiply 160 and 125 to get 20000.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{20000}{2}p)$$

Divide 20000 by 2 to get 10000.

$$\frac{\mathrm{d}}{\mathrm{d}p}(10000p)$$

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

$$10000p^{1-1}$$

Subtract 1 from 1.

$$10000p^{0}$$

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

$$10000\times 1$$

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

$$10000$$