Solve x*5.0*10^2

$$x \times 5.0 \times { 10 }^{ 2 }$$

Evaluate

$$500x$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$x\times 5\times 100$$

Multiply 5 and 100 to get 500.

$$x\times 500$$

Differentiate w.r.t. x

$$500$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 5\times 100)$$

Multiply 5 and 100 to get 500.

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

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

$$500x^{1-1}$$

Subtract 1 from 1.

$$500x^{0}$$

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

$$500\times 1$$

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

$$500$$