Solve (3x-8)+(5-6x^2-8x)

$$( 3 x - 8 ) + ( 5 - 6 x ^ { 2 } - 8 x )$$

Evaluate

$$-6x^{2}-5x-3$$

Solution Steps

Add -8 and 5 to get -3.

$$3x-3-6x^{2}-8x$$

Combine 3x and -8x to get -5x.

$$-5x-3-6x^{2}$$

Differentiate w.r.t. x

$$-12x-5$$

Steps Using Derivative Rule for Sum

Add -8 and 5 to get -3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x-3-6x^{2}-8x)$$

Combine 3x and -8x to get -5x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x-3-6x^{2})$$

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}.

$$-5x^{1-1}+2\left(-6\right)x^{2-1}$$

Subtract 1 from 1.

$$-5x^{0}+2\left(-6\right)x^{2-1}$$

Multiply 2 times -6.

$$-5x^{0}-12x^{2-1}$$

Subtract 1 from 2.

$$-5x^{0}-12x^{1}$$

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

$$-5x^{0}-12x$$

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

$$-5-12x$$