Solve -d^3+10d^2-28d+84

$$- d ^ { 3 } + 10 d ^ { 2 } - 28 d + 84$$

Differentiate w.r.t. d

$$\left(2-d\right)\left(3d-14\right)$$

Steps Using Derivative Rule for Sum

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}.

$$3\left(-1\right)d^{3-1}+2\times 10d^{2-1}-28d^{1-1}$$

Multiply 3 times -1.

$$-3d^{3-1}+2\times 10d^{2-1}-28d^{1-1}$$

Subtract 1 from 3.

$$-3d^{2}+2\times 10d^{2-1}-28d^{1-1}$$

Multiply 2 times 10.

$$-3d^{2}+20d^{2-1}-28d^{1-1}$$

Subtract 1 from 2.

$$-3d^{2}+20d^{1}-28d^{1-1}$$

Subtract 1 from 1.

$$-3d^{2}+20d^{1}-28d^{0}$$

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

$$-3d^{2}+20d-28d^{0}$$

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

$$-3d^{2}+20d-28$$

Evaluate

$$84-28d+10d^{2}-d^{3}$$