Solve 400000*10^2ndiv12*3=

$$400000 \times 10 ^ { 2 } n \div 12 \times 3 =$$

Evaluate

$$10000000n$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\frac{400000\times 100n}{12}\times 3$$

Multiply 400000 and 100 to get 40000000.

$$\frac{40000000n}{12}\times 3$$

Divide 40000000n by 12 to get \frac{10000000}{3}n.

$$\frac{10000000}{3}n\times 3$$

Cancel out 3 and 3.

$$10000000n$$

Differentiate w.r.t. n

$$10000000$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{400000\times 100n}{12}\times 3)$$

Multiply 400000 and 100 to get 40000000.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{40000000n}{12}\times 3)$$

Divide 40000000n by 12 to get \frac{10000000}{3}n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{10000000}{3}n\times 3)$$

Cancel out 3 and 3.

$$\frac{\mathrm{d}}{\mathrm{d}n}(10000000n)$$

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

$$10000000n^{1-1}$$

Subtract 1 from 1.

$$10000000n^{0}$$

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

$$10000000\times 1$$

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

$$10000000$$