Solve 3/9P*150/82*300=

$$\frac { \frac { 3 } { 9 } P \times 150 } { 82 \times 300 } =$$

Evaluate

$$\frac{P}{492}$$

Solution Steps

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{3}P\times 150}{82\times 300}$$

Multiply \frac{1}{3} and 150 to get \frac{150}{3}.

$$\frac{\frac{150}{3}P}{82\times 300}$$

Divide 150 by 3 to get 50.

$$\frac{50P}{82\times 300}$$

Multiply 82 and 300 to get 24600.

$$\frac{50P}{24600}$$

Divide 50P by 24600 to get \frac{1}{492}P.

$$\frac{1}{492}P$$

Differentiate w.r.t. P

$$\frac{1}{492} = 0.0020325203252032522$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{3}{9} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}P}(\frac{\frac{1}{3}P\times 150}{82\times 300})$$

Multiply \frac{1}{3} and 150 to get \frac{150}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}P}(\frac{\frac{150}{3}P}{82\times 300})$$

Divide 150 by 3 to get 50.

$$\frac{\mathrm{d}}{\mathrm{d}P}(\frac{50P}{82\times 300})$$

Multiply 82 and 300 to get 24600.

$$\frac{\mathrm{d}}{\mathrm{d}P}(\frac{50P}{24600})$$

Divide 50P by 24600 to get \frac{1}{492}P.

$$\frac{\mathrm{d}}{\mathrm{d}P}(\frac{1}{492}P)$$

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

$$\frac{1}{492}P^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{492}P^{0}$$

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

$$\frac{1}{492}\times 1$$

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

$$\frac{1}{492}$$