Solve 8x(-5x)

$$8 x ( - 5 x )$$

Evaluate

$$-40x^{2}$$

Solution Steps

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

$$8x^{2}\left(-5\right)$$

Multiply 8 and -5 to get -40.

$$-40x^{2}$$

Differentiate w.r.t. x

$$-80x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{2}\left(-5\right))$$

Multiply 8 and -5 to get -40.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-40x^{2})$$

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

$$2\left(-40\right)x^{2-1}$$

Multiply 2 times -40.

$$-80x^{2-1}$$

Subtract 1 from 2.

$$-80x^{1}$$

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

$$-80x$$