Solve R(x)=4x-01x^2

$$R ( x ) = 4 x - 01 x ^ { 2 }$$

Evaluate

$$4x$$

Solution Steps

Multiply 0 and 1 to get 0.

$$4x-0x^{2}$$

Anything times zero gives zero.

$$4x-0$$

Differentiate w.r.t. x

$$4$$

Steps Using Definition of a Derivative

Multiply 0 and 1 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x-0x^{2})$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x-0)$$

Multiply -1 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+0)$$

Anything plus zero gives itself.

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

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

$$4x^{1-1}$$

Subtract 1 from 1.

$$4x^{0}$$

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

$$4\times 1$$

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

$$4$$