Solve 9x^2-3x-56x^2-8x-1

$$9 x ^ { 2 } - 3 x - 56 x ^ { 2 } - 8 x - 1$$

Evaluate

$$-47x^{2}-11x-1$$

Solution Steps

Combine 9x^{2} and -56x^{2} to get -47x^{2}.

$$-47x^{2}-3x-8x-1$$

Combine -3x and -8x to get -11x.

$$-47x^{2}-11x-1$$

Differentiate w.r.t. x

$$-94x-11$$

Steps Using Derivative Rule for Sum

Combine 9x^{2} and -56x^{2} to get -47x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-47x^{2}-3x-8x-1)$$

Combine -3x and -8x to get -11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-47x^{2}-11x-1)$$

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}.

$$2\left(-47\right)x^{2-1}-11x^{1-1}$$

Multiply 2 times -47.

$$-94x^{2-1}-11x^{1-1}$$

Subtract 1 from 2.

$$-94x^{1}-11x^{1-1}$$

Subtract 1 from 1.

$$-94x^{1}-11x^{0}$$

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

$$-94x-11x^{0}$$

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

$$-94x-11$$