Solve (4x^2-9x-3)+(x^2+5x+6)=

$$( 4 x ^ { 2 } - 9 x - 3 ) + ( x ^ { 2 } + 5 x + 6 ) =$$

Evaluate

$$5x^{2}-4x+3$$

Solution Steps

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$5x^{2}-9x-3+5x+6$$

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

$$5x^{2}-4x-3+6$$

Add -3 and 6 to get 3.

$$5x^{2}-4x+3$$

Differentiate w.r.t. x

$$10x-4$$

Steps Using Derivative Rule for Sum

Combine 4x^{2} and x^{2} to get 5x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-9x-3+5x+6)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-4x-3+6)$$

Add -3 and 6 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}-4x+3)$$

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}.

$$2\times 5x^{2-1}-4x^{1-1}$$

Multiply 2 times 5.

$$10x^{2-1}-4x^{1-1}$$

Subtract 1 from 2.

$$10x^{1}-4x^{1-1}$$

Subtract 1 from 1.

$$10x^{1}-4x^{0}$$

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

$$10x-4x^{0}$$

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

$$10x-4$$