Solve (9x-3y+5)+(-x-y+4)+(-5x+4y-9)

$$( 9 x - 3 y + 5 ) + ( - x - y + 4 ) + ( - 5 x + 4 y - 9 )$$

Evaluate

$$3x$$

Solution Steps

Combine -3y and -y to get -4y.

$$9x-4y+5-x+4-5x+4y-9$$

Add 5 and 4 to get 9.

$$9x-4y+9-x-5x+4y-9$$

Combine 9x and -5x to get 4x.

$$4x-4y+9-x+4y-9$$

Combine -4y and 4y to get 0.

$$4x+9-x-9$$

Subtract 9 from 9 to get 0.

$$4x-x$$

Combine 4x and -x to get 3x.

$$3x$$

Differentiate w.r.t. x

$$3$$

Steps Using Definition of a Derivative

Combine -3y and -y to get -4y.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-4y+5-x+4-5x+4y-9)$$

Add 5 and 4 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x-4y+9-x-5x+4y-9)$$

Combine 9x and -5x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x-4y+9-x+4y-9)$$

Combine -4y and 4y to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+9-x-9)$$

Subtract 9 from 9 to get 0.

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

Combine 4x and -x to get 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x)$$

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

$$3x^{1-1}$$

Subtract 1 from 1.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$