Solve 5x(-4)^2-2(-9)+3

$$5 x ( - 4 ) ^ { 2 } - 2 ( - 9 ) + 3$$

Evaluate

$$80x+21$$

Solution Steps

Calculate -4 to the power of 2 and get 16.

$$5x\times 16-2\left(-9\right)+3$$

Multiply 5 and 16 to get 80.

$$80x-2\left(-9\right)+3$$

Multiply 2 and -9 to get -18.

$$80x-\left(-18\right)+3$$

The opposite of -18 is 18.

$$80x+18+3$$

Add 18 and 3 to get 21.

$$80x+21$$

Differentiate w.r.t. x

$$80$$

Steps Using Derivative Rule for Sum

Calculate -4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x\times 16-2\left(-9\right)+3)$$

Multiply 5 and 16 to get 80.

$$\frac{\mathrm{d}}{\mathrm{d}x}(80x-2\left(-9\right)+3)$$

Multiply 2 and -9 to get -18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(80x-\left(-18\right)+3)$$

The opposite of -18 is 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(80x+18+3)$$

Add 18 and 3 to get 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(80x+21)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

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

Subtract 1 from 1.

$$80x^{0}$$

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

$$80\times 1$$

For any term t, t\times 1=t and 1t=t.

$$80$$