Solve 16p^4+4p^2-12p+9

$$16 p ^ { 4 } + 4 p ^ { 2 } - 12 p + 9$$

Differentiate w.r.t. p

$$64p^{3}+8p-12$$

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}.

$$4\times 16p^{4-1}+2\times 4p^{2-1}-12p^{1-1}$$

Multiply 4 times 16.

$$64p^{4-1}+2\times 4p^{2-1}-12p^{1-1}$$

Subtract 1 from 4.

$$64p^{3}+2\times 4p^{2-1}-12p^{1-1}$$

Multiply 2 times 4.

$$64p^{3}+8p^{2-1}-12p^{1-1}$$

Subtract 1 from 2.

$$64p^{3}+8p^{1}-12p^{1-1}$$

Subtract 1 from 1.

$$64p^{3}+8p^{1}-12p^{0}$$

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

$$64p^{3}+8p-12p^{0}$$

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

$$64p^{3}+8p-12$$

Evaluate

$$16p^{4}+\left(2p-3\right)^{2}$$