Solve (4x10^2

$$(4x { 10 }^{ 2 }$$

Evaluate

$$400x$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$4x\times 100$$

Multiply 4 and 100 to get 400.

$$400x$$

Differentiate w.r.t. x

$$400$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x\times 100)$$

Multiply 4 and 100 to get 400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(400x)$$

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

$$400x^{1-1}$$

Subtract 1 from 1.

$$400x^{0}$$

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

$$400\times 1$$

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

$$400$$