Solve 1/4x*-3x

$$\frac{ 1 }{ 4 } x \times -3x$$

Evaluate

$$-\frac{3x^{2}}{4}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{1}{4}x^{2}\left(-3\right)$$

Multiply \frac{1}{4} and -3 to get \frac{-3}{4}.

$$\frac{-3}{4}x^{2}$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$-\frac{3}{4}x^{2}$$

Differentiate w.r.t. x

$$-\frac{3x}{2}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4}x^{2}\left(-3\right))$$

Multiply \frac{1}{4} and -3 to get \frac{-3}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3}{4}x^{2})$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{3}{4}x^{2})$$

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

$$2\left(-\frac{3}{4}\right)x^{2-1}$$

Multiply 2 times -\frac{3}{4}.

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

Subtract 1 from 2.

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

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

$$-\frac{3}{2}x$$