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

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

Evaluate

$$11x^{2}-3x+5$$

Solution Steps

Combine 5x^{2} and 6x^{2} to get 11x^{2}.

$$11x^{2}-4x+5+x$$

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

$$11x^{2}-3x+5$$

Differentiate w.r.t. x

$$22x-3$$

Steps Using Derivative Rule for Sum

Combine 5x^{2} and 6x^{2} to get 11x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{2}-4x+5+x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{2}-3x+5)$$

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}.

$$2\times 11x^{2-1}-3x^{1-1}$$

Multiply 2 times 11.

$$22x^{2-1}-3x^{1-1}$$

Subtract 1 from 2.

$$22x^{1}-3x^{1-1}$$

Subtract 1 from 1.

$$22x^{1}-3x^{0}$$

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

$$22x-3x^{0}$$

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

$$22x-3$$