Solve +0x^3+3x^2

$$+ 0 x ^ { 3 } + 3 x ^ { 2 }$$

Evaluate

$$3x^{2}$$

Solution Steps

Anything times zero gives zero.

$$0+3x^{2}$$

Anything plus zero gives itself.

$$3x^{2}$$

Differentiate w.r.t. x

$$6x$$

Steps Using Definition of a Derivative

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}x}(0+3x^{2})$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2})$$

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

$$2\times 3x^{2-1}$$

Multiply 2 times 3.

$$6x^{2-1}$$

Subtract 1 from 2.

$$6x^{1}$$

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

$$6x$$