Solve 9x*0,5+2*4x-4,5x

$$9 x \times 0,5 + 2 \times 4 x - 4,5 x$$

Evaluate

$$8x$$

Solution Steps

Multiply 9 and 0,5 to get 4,5.

$$4,5x+2\times 4x-4,5x$$

Multiply 2 and 4 to get 8.

$$4,5x+8x-4,5x$$

Combine 4,5x and 8x to get 12,5x.

$$12,5x-4,5x$$

Combine 12,5x and -4,5x to get 8x.

$$8x$$

Differentiate w.r.t. x

$$8$$

Steps Using Definition of a Derivative

Multiply 9 and 0,5 to get 4,5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4,5x+2\times 4x-4,5x)$$

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4,5x+8x-4,5x)$$

Combine 4,5x and 8x to get 12,5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12,5x-4,5x)$$

Combine 12,5x and -4,5x to get 8x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x)$$

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

$$8x^{1-1}$$

Subtract 1 from 1.

$$8x^{0}$$

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

$$8\times 1$$

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

$$8$$