Solve -20x(-2)^2+9x(-2)

$$- 20 x ( - 2 ) ^ { 2 } + 9 x ( - 2 )$$

Evaluate

$$-98x$$

Solution Steps

Calculate -2 to the power of 2 and get 4.

$$-20x\times 4+9x\left(-2\right)$$

Multiply -20 and 4 to get -80.

$$-80x+9x\left(-2\right)$$

Multiply 9 and -2 to get -18.

$$-80x-18x$$

Combine -80x and -18x to get -98x.

$$-98x$$

Differentiate w.r.t. x

$$-98$$

Steps Using Definition of a Derivative

Calculate -2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-20x\times 4+9x\left(-2\right))$$

Multiply -20 and 4 to get -80.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-80x+9x\left(-2\right))$$

Multiply 9 and -2 to get -18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-80x-18x)$$

Combine -80x and -18x to get -98x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-98x)$$

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

$$-98x^{1-1}$$

Subtract 1 from 1.

$$-98x^{0}$$

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

$$-98$$