Solve (x^2+6x+4)+(-9x+1)

$$( x ^ { 2 } + 6 x + 4 ) + ( - 9 x + 1 )$$

Evaluate

$$x^{2}-3x+5$$

Solution Steps

Combine 6x and -9x to get -3x.

$$x^{2}-3x+4+1$$

Add 4 and 1 to get 5.

$$x^{2}-3x+5$$

Differentiate w.r.t. x

$$2x-3$$

Steps Using Derivative Rule for Sum

Combine 6x and -9x to get -3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-3x+4+1)$$

Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-3x+5)$$

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}.

$$2x^{2-1}-3x^{1-1}$$

Subtract 1 from 2.

$$2x^{1}-3x^{1-1}$$

Subtract 1 from 1.

$$2x^{1}-3x^{0}$$

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

$$2x-3x^{0}$$

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

$$2x-3$$