Solve 12x^2+9-5x-7x^2-6x

$$12 x ^ { 2 } + 9 - 5 x - 7 x ^ { 2 } - 6 x$$

Evaluate

$$5x^{2}-11x+9$$

Solution Steps

Combine 12x^{2} and -7x^{2} to get 5x^{2}.

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

Combine -5x and -6x to get -11x.

$$5x^{2}+9-11x$$

Differentiate w.r.t. x

$$10x-11$$

Steps Using Derivative Rule for Sum

Combine 12x^{2} and -7x^{2} to get 5x^{2}.

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

Combine -5x and -6x to get -11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}+9-11x)$$

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}.

$$2\times 5x^{2-1}-11x^{1-1}$$

Multiply 2 times 5.

$$10x^{2-1}-11x^{1-1}$$

Subtract 1 from 2.

$$10x^{1}-11x^{1-1}$$

Subtract 1 from 1.

$$10x^{1}-11x^{0}$$

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

$$10x-11x^{0}$$

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

$$10x-11$$