Solve 7x^2-3x+10+4x^2-6x+4

$$7 { x }^{ 2 } -3x+10+4 { x }^{ 2 } -6x+4$$

Evaluate

$$11x^{2}-9x+14$$

Solution Steps

Combine 7x^{2} and 4x^{2} to get 11x^{2}.

$$11x^{2}-3x+10-6x+4$$

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

$$11x^{2}-9x+10+4$$

Add 10 and 4 to get 14.

$$11x^{2}-9x+14$$

Differentiate w.r.t. x

$$22x-9$$

Steps Using Derivative Rule for Sum

Combine 7x^{2} and 4x^{2} to get 11x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{2}-3x+10-6x+4)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{2}-9x+10+4)$$

Add 10 and 4 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{2}-9x+14)$$

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}.

$$2\times 11x^{2-1}-9x^{1-1}$$

Multiply 2 times 11.

$$22x^{2-1}-9x^{1-1}$$

Subtract 1 from 2.

$$22x^{1}-9x^{1-1}$$

Subtract 1 from 1.

$$22x^{1}-9x^{0}$$

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

$$22x-9x^{0}$$

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

$$22x-9$$