Solve f(x)=5x+1quadf(0)=

$$f ( x ) = 5 x + 1 \quad f ( 0 ) =$$

Evaluate

$$5x$$

Solution Steps

Multiply 1 and 0 to get 0.

$$5x+0f$$

Anything times zero gives zero.

$$5x+0$$

Anything plus zero gives itself.

$$5x$$

Differentiate w.r.t. x

$$5$$

Steps Using Definition of a Derivative

Multiply 1 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x+0f)$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x+0)$$

Anything plus zero gives itself.

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

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

$$5x^{1-1}$$

Subtract 1 from 1.

$$5x^{0}$$

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

$$5\times 1$$

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

$$5$$