Solve 0.9x+x+0.7x+0.3x+0.2x

$$0.9 x + x + 0.7 x + 0.3 x + 0.2 x$$

Evaluate

$$\frac{31x}{10}$$

Solution Steps

Combine 0.9x and x to get 1.9x.

$$1.9x+0.7x+0.3x+0.2x$$

Combine 1.9x and 0.7x to get 2.6x.

$$2.6x+0.3x+0.2x$$

Combine 2.6x and 0.3x to get 2.9x.

$$2.9x+0.2x$$

Combine 2.9x and 0.2x to get 3.1x.

$$3.1x$$

Differentiate w.r.t. x

$$3.1$$

Steps Using Definition of a Derivative

Combine 0.9x and x to get 1.9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1.9x+0.7x+0.3x+0.2x)$$

Combine 1.9x and 0.7x to get 2.6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2.6x+0.3x+0.2x)$$

Combine 2.6x and 0.3x to get 2.9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2.9x+0.2x)$$

Combine 2.9x and 0.2x to get 3.1x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3.1x)$$

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

$$3.1x^{1-1}$$

Subtract 1 from 1.

$$3.1x^{0}$$

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

$$3.1\times 1$$

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

$$3.1$$