Solve (7x+4-4x^2)+(5+5x^2-4x)

$$( 7 x + 4 - 4 x ^ { 2 } ) + ( 5 + 5 x ^ { 2 } - 4 x )$$

Evaluate

$$x^{2}+3x+9$$

Solution Steps

Add 4 and 5 to get 9.

$$7x+9-4x^{2}+5x^{2}-4x$$

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

$$7x+9+x^{2}-4x$$

Combine 7x and -4x to get 3x.

$$3x+9+x^{2}$$

Differentiate w.r.t. x

$$2x+3$$

Steps Using Derivative Rule for Sum

Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x+9-4x^{2}+5x^{2}-4x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x+9+x^{2}-4x)$$

Combine 7x and -4x to get 3x.

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

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}.

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

Subtract 1 from 1.

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

Subtract 1 from 2.

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

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

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

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

$$3\times 1+2x$$

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

$$3+2x$$