Solve (-44x^2+6x-24)+(17x^2-35x-23)

$$( - 44 x ^ { 2 } + 6 x - 24 ) + ( 17 x ^ { 2 } - 35 x - 23 )$$

Evaluate

$$-27x^{2}-29x-47$$

Solution Steps

Combine -44x^{2} and 17x^{2} to get -27x^{2}.

$$-27x^{2}+6x-24-35x-23$$

Combine 6x and -35x to get -29x.

$$-27x^{2}-29x-24-23$$

Subtract 23 from -24 to get -47.

$$-27x^{2}-29x-47$$

Differentiate w.r.t. x

$$-54x-29$$

Steps Using Derivative Rule for Sum

Combine -44x^{2} and 17x^{2} to get -27x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-27x^{2}+6x-24-35x-23)$$

Combine 6x and -35x to get -29x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-27x^{2}-29x-24-23)$$

Subtract 23 from -24 to get -47.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-27x^{2}-29x-47)$$

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}.

$$2\left(-27\right)x^{2-1}-29x^{1-1}$$

Multiply 2 times -27.

$$-54x^{2-1}-29x^{1-1}$$

Subtract 1 from 2.

$$-54x^{1}-29x^{1-1}$$

Subtract 1 from 1.

$$-54x^{1}-29x^{0}$$

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

$$-54x-29x^{0}$$

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

$$-54x-29$$