Solve 36p^2qdiv(-9pq)

$$36 p ^ { 2 } q \div ( - 9 p q )$$

Evaluate

$$-4p$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{36^{1}p^{2}q^{1}}{\left(-9\right)^{1}p^{1}q^{1}}$$

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

$$\frac{36^{1}}{\left(-9\right)^{1}}p^{2-1}q^{1-1}$$

Subtract 1 from 2.

$$\frac{36^{1}}{\left(-9\right)^{1}}p^{1}q^{1-1}$$

Subtract 1 from 1.

$$\frac{36^{1}}{\left(-9\right)^{1}}pq^{0}$$

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

$$\frac{36^{1}}{\left(-9\right)^{1}}p$$

Divide 36 by -9.

$$-4p$$

Differentiate w.r.t. p

$$-4$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\frac{36q}{-9q}p^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-4p^{1})$$

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}.

$$-4p^{1-1}$$

Do the arithmetic.

$$-4p^{0}$$

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

$$-4$$