Solve 30div0.86*100n

$$30 \div 0.86 \times 100 n$$

Evaluate

$$\frac{150000n}{43}$$

Solution Steps

Expand \frac{30}{0.86} by multiplying both numerator and the denominator by 100.

$$\frac{3000}{86}\times 100n$$

Reduce the fraction \frac{3000}{86} to lowest terms by extracting and canceling out 2.

$$\frac{1500}{43}\times 100n$$

Express \frac{1500}{43}\times 100 as a single fraction.

$$\frac{1500\times 100}{43}n$$

Multiply 1500 and 100 to get 150000.

$$\frac{150000}{43}n$$

Differentiate w.r.t. n

$$\frac{150000}{43} = 3488\frac{16}{43} = 3488.3720930232557$$

Steps Using Definition of a Derivative

Expand \frac{30}{0.86} by multiplying both numerator and the denominator by 100.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3000}{86}\times 100n)$$

Reduce the fraction \frac{3000}{86} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1500}{43}\times 100n)$$

Express \frac{1500}{43}\times 100 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1500\times 100}{43}n)$$

Multiply 1500 and 100 to get 150000.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{150000}{43}n)$$

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

$$\frac{150000}{43}n^{1-1}$$

Subtract 1 from 1.

$$\frac{150000}{43}n^{0}$$

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

$$\frac{150000}{43}\times 1$$

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

$$\frac{150000}{43}$$