Solve 4z^3-35z^2+16z-40

$$4 z ^ { 3 } - 35 z ^ { 2 } + 16 z - 40$$

Differentiate w.r.t. z

$$12z^{2}-70z+16$$

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}.

$$3\times 4z^{3-1}+2\left(-35\right)z^{2-1}+16z^{1-1}$$

Multiply 3 times 4.

$$12z^{3-1}+2\left(-35\right)z^{2-1}+16z^{1-1}$$

Subtract 1 from 3.

$$12z^{2}+2\left(-35\right)z^{2-1}+16z^{1-1}$$

Multiply 2 times -35.

$$12z^{2}-70z^{2-1}+16z^{1-1}$$

Subtract 1 from 2.

$$12z^{2}-70z^{1}+16z^{1-1}$$

Subtract 1 from 1.

$$12z^{2}-70z^{1}+16z^{0}$$

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

$$12z^{2}-70z+16z^{0}$$

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

$$12z^{2}-70z+16\times 1$$

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

$$12z^{2}-70z+16$$

Evaluate

$$4z^{3}-35z^{2}+16z-40$$