Solve 2x10^3+2x10^2

$$2x { 10 }^{ 3 } +2x { 10 }^{ 2 }$$

Evaluate

$$2200x$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$2x\times 1000+2x\times 10^{2}$$

Multiply 2 and 1000 to get 2000.

$$2000x+2x\times 10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$2000x+2x\times 100$$

Multiply 2 and 100 to get 200.

$$2000x+200x$$

Combine 2000x and 200x to get 2200x.

$$2200x$$

Differentiate w.r.t. x

$$2200$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 3 and get 1000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x\times 1000+2x\times 10^{2})$$

Multiply 2 and 1000 to get 2000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2000x+2x\times 10^{2})$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2000x+2x\times 100)$$

Multiply 2 and 100 to get 200.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2000x+200x)$$

Combine 2000x and 200x to get 2200x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2200x)$$

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

$$2200x^{1-1}$$

Subtract 1 from 1.

$$2200x^{0}$$

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

$$2200\times 1$$

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

$$2200$$