Solve p^3q^3*p^2q^2-pq+1=

$$p ^ { 3 } q ^ { 3 } \cdot p ^ { 2 } q ^ { 2 } - p q + 1 =$$

Differentiate w.r.t. p

$$q\left(5\left(pq\right)^{4}-1\right)$$

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}.

$$3p^{2}q^{2}q^{3}p^{3-1}+\left(-q\right)p^{1-1}$$

Multiply 3 times q^{3}p^{2}q^{2}.

$$3p^{2}q^{5}p^{3-1}+\left(-q\right)p^{1-1}$$

Subtract 1 from 3.

$$3p^{2}q^{5}p^{2}+\left(-q\right)p^{1-1}$$

Subtract 1 from 1.

$$3p^{2}q^{5}p^{2}+\left(-q\right)p^{0}$$

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

$$3p^{2}q^{5}p^{2}+\left(-q\right)\times 1$$

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

$$3p^{2}q^{5}p^{2}-q$$

Evaluate

$$1+\left(pq\right)^{5}-pq$$