Solve 5x(-2)^2+4.5

$$5 x ( - 2 ) ^ { 2 } + 4.5$$

Evaluate

$$20x+4.5$$

Solution Steps

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

$$5x\times 4+4.5$$

Multiply 5 and 4 to get 20.

$$20x+4.5$$

Differentiate w.r.t. x

$$20$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x\times 4+4.5)$$

Multiply 5 and 4 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20x+4.5)$$

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}.

$$20x^{1-1}$$

Subtract 1 from 1.

$$20x^{0}$$

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

$$20\times 1$$

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

$$20$$