Solve {l}{27y^3}{+9y^2+9y+1}

$$\left. \begin{array} { l } { 27 y ^ { 3 } } \\ { + 9 y ^ { 2 } + 9 y + 1 } \end{array} \right.$$

Differentiate w.r.t. y

$$81y^{2}+18y+9$$

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}.

$$3\times 27y^{3-1}+2\times 9y^{2-1}+9y^{1-1}$$

Multiply 3 times 27.

$$81y^{3-1}+2\times 9y^{2-1}+9y^{1-1}$$

Subtract 1 from 3.

$$81y^{2}+2\times 9y^{2-1}+9y^{1-1}$$

Multiply 2 times 9.

$$81y^{2}+18y^{2-1}+9y^{1-1}$$

Subtract 1 from 2.

$$81y^{2}+18y^{1}+9y^{1-1}$$

Subtract 1 from 1.

$$81y^{2}+18y^{1}+9y^{0}$$

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

$$81y^{2}+18y+9y^{0}$$

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

$$81y^{2}+18y+9\times 1$$

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

$$81y^{2}+18y+9$$

Evaluate

$$27y^{3}+9y^{2}+9y+1$$