Solve d/dx(0.1(400-40x+x^2))

$$\frac { d } { d x } ( 0.1 ( 400 - 40 x + x ^ { 2 } ) )$$

Evaluate

$$\frac{x}{5}-4$$

Steps Using Derivative Rule for Sum

Use the distributive property to multiply 0.1 by 400-40x+x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(40-4x+0.1x^{2})$$

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}.

$$-4x^{1-1}+2\times 0.1x^{2-1}$$

Subtract 1 from 1.

$$-4x^{0}+2\times 0.1x^{2-1}$$

Multiply 2 times 0.1.

$$-4x^{0}+0.2x^{2-1}$$

Subtract 1 from 2.

$$-4x^{0}+0.2x^{1}$$

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

$$-4x^{0}+0.2x$$

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

$$-4+0.2x$$

Differentiate w.r.t. x

$$0.2$$