Solve -9x^2+3+6x-4-10x^2

$$- 9 x ^ { 2 } + 3 + 6 x - 4 - 10 x ^ { 2 }$$

Evaluate

$$-19x^{2}+6x-1$$

Solution Steps

Subtract 4 from 3 to get -1.

$$-9x^{2}-1+6x-10x^{2}$$

Combine -9x^{2} and -10x^{2} to get -19x^{2}.

$$-19x^{2}-1+6x$$

Differentiate w.r.t. x

$$6-38x$$

Steps Using Derivative Rule for Sum

Subtract 4 from 3 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-9x^{2}-1+6x-10x^{2})$$

Combine -9x^{2} and -10x^{2} to get -19x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-19x^{2}-1+6x)$$

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}.

$$2\left(-19\right)x^{2-1}+6x^{1-1}$$

Multiply 2 times -19.

$$-38x^{2-1}+6x^{1-1}$$

Subtract 1 from 2.

$$-38x^{1}+6x^{1-1}$$

Subtract 1 from 1.

$$-38x^{1}+6x^{0}$$

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

$$-38x+6x^{0}$$

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

$$-38x+6\times 1$$

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

$$-38x+6$$