Solve 100^2*500/2*2*12x

$${ 100 }^{ 2 } \times \frac{ 500 }{ 2 \times 2 } \times 12x$$

Evaluate

$$15000000x$$

Solution Steps

Calculate 100 to the power of 2 and get 10000.

$$10000\times \frac{500}{2\times 2}\times 12x$$

Multiply 2 and 2 to get 4.

$$10000\times \frac{500}{4}\times 12x$$

Divide 500 by 4 to get 125.

$$10000\times 125\times 12x$$

Multiply 10000 and 125 to get 1250000.

$$1250000\times 12x$$

Multiply 1250000 and 12 to get 15000000.

$$15000000x$$

Differentiate w.r.t. x

$$15000000$$

Steps Using Definition of a Derivative

Calculate 100 to the power of 2 and get 10000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10000\times \frac{500}{2\times 2}\times 12x)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10000\times \frac{500}{4}\times 12x)$$

Divide 500 by 4 to get 125.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10000\times 125\times 12x)$$

Multiply 10000 and 125 to get 1250000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1250000\times 12x)$$

Multiply 1250000 and 12 to get 15000000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15000000x)$$

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

$$15000000x^{1-1}$$

Subtract 1 from 1.

$$15000000x^{0}$$

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

$$15000000\times 1$$

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

$$15000000$$