Solve 4x(-5x)

$$4 x ( - 5 x )$$

Evaluate

$$-20x^{2}$$

Solution Steps

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

$$4x^{2}\left(-5\right)$$

Multiply 4 and -5 to get -20.

$$-20x^{2}$$

Differentiate w.r.t. x

$$-40x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}\left(-5\right))$$

Multiply 4 and -5 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-20x^{2})$$

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

$$2\left(-20\right)x^{2-1}$$

Multiply 2 times -20.

$$-40x^{2-1}$$

Subtract 1 from 2.

$$-40x^{1}$$

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

$$-40x$$