Solve 2x^2:1/2=

$$2 x ^ { 2 } : \frac { 1 } { 2 } =$$

Evaluate

$$4x^{2}$$

Solution Steps

Divide 2x^{2} by \frac{1}{2} by multiplying 2x^{2} by the reciprocal of \frac{1}{2}.

$$2x^{2}\times 2$$

Multiply 2 and 2 to get 4.

$$4x^{2}$$

Differentiate w.r.t. x

$$8x$$

Steps Using Definition of a Derivative

Divide 2x^{2} by \frac{1}{2} by multiplying 2x^{2} by the reciprocal of \frac{1}{2}.

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

Multiply 2 and 2 to get 4.

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

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

$$2\times 4x^{2-1}$$

Multiply 2 times 4.

$$8x^{2-1}$$

Subtract 1 from 2.

$$8x^{1}$$

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

$$8x$$