Solve 3pq^3*4p^4q/(-2pq)(-3pq)

$$\frac { 3 p q ^ { 3 } \times 4 p ^ { 4 } q } { ( - 2 p q ) ( - 3 p q ) }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{3p^{5}q^{3}\times 4q}{-2pq\left(-3\right)pq}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{3p^{5}q^{4}\times 4}{-2pq\left(-3\right)pq}$$

Multiply p and p to get p^{2}.

$$\frac{3p^{5}q^{4}\times 4}{-2p^{2}q\left(-3\right)q}$$

Multiply q and q to get q^{2}.

$$\frac{3p^{5}q^{4}\times 4}{-2p^{2}q^{2}\left(-3\right)}$$

Cancel out 2\times 3p^{2}q^{2} in both numerator and denominator.

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

Multiply -1 and -1 to get 1.

$$\frac{2q^{2}p^{3}}{1}$$

Anything divided by one gives itself.

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

Differentiate w.r.t. p

$$6\left(pq\right)^{2}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{12p^{4}q^{4}}{6pq^{2}}p^{1-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(2q^{2}p^{3}p^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}p}(2q^{2}p^{3})$$

The derivative of a constant term is 0.

$$0$$