Solve 4y^3-2y^2+4y+1

$$4 { y }^{ 3 } -2 { y }^{ 2 } +4y+1$$

Differentiate w.r.t. y

$$12y^{2}-4y+4$$

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}.

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

Multiply 3 times 4.

$$12y^{3-1}+2\left(-2\right)y^{2-1}+4y^{1-1}$$

Subtract 1 from 3.

$$12y^{2}+2\left(-2\right)y^{2-1}+4y^{1-1}$$

Multiply 2 times -2.

$$12y^{2}-4y^{2-1}+4y^{1-1}$$

Subtract 1 from 2.

$$12y^{2}-4y^{1}+4y^{1-1}$$

Subtract 1 from 1.

$$12y^{2}-4y^{1}+4y^{0}$$

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

$$12y^{2}-4y+4y^{0}$$

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

$$12y^{2}-4y+4\times 1$$

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

$$12y^{2}-4y+4$$

Evaluate

$$4y^{3}-2y^{2}+4y+1$$