Solve -3x*-4+5y*0

$$- 3 x \cdot - 4 + 5 y \cdot 0$$

Evaluate

$$12x$$

Solution Steps

Multiply -3 and -4 to get 12.

$$12x+5y\times 0$$

Multiply 5 and 0 to get 0.

$$12x+0y$$

Anything times zero gives zero.

$$12x+0$$

Anything plus zero gives itself.

$$12x$$

Differentiate w.r.t. x

$$12$$

Steps Using Definition of a Derivative

Multiply -3 and -4 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x+5y\times 0)$$

Multiply 5 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x+0y)$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x+0)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x)$$

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

$$12x^{1-1}$$

Subtract 1 from 1.

$$12x^{0}$$

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

$$12\times 1$$

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

$$12$$