Solve 1/2(8x)(6*-5)

$$\frac{ 1 }{ 2 } (8x)(6 \times -5)$$

Evaluate

$$-120x$$

Solution Steps

Multiply \frac{1}{2} and 8 to get \frac{8}{2}.

$$\frac{8}{2}x\times 6\left(-5\right)$$

Divide 8 by 2 to get 4.

$$4x\times 6\left(-5\right)$$

Multiply 4 and 6 to get 24.

$$24x\left(-5\right)$$

Multiply 24 and -5 to get -120.

$$-120x$$

Differentiate w.r.t. x

$$-120$$

Steps Using Definition of a Derivative

Multiply \frac{1}{2} and 8 to get \frac{8}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{2}x\times 6\left(-5\right))$$

Divide 8 by 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x\times 6\left(-5\right))$$

Multiply 4 and 6 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x\left(-5\right))$$

Multiply 24 and -5 to get -120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-120x)$$

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

$$-120x^{1-1}$$

Subtract 1 from 1.

$$-120x^{0}$$

For any term t except 0, t^{0}=1.

$$-120$$