Solve -30p^2/6pq

$$\frac { - 30 p ^ { 2 } } { 6 p q }$$

Differentiate w.r.t. p

$$-\frac{5}{q}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}p}(\left(-\frac{30}{6q}\right)p^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}p}(\left(-\frac{5}{q}\right)p^{1})$$

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}.

$$\left(-\frac{5}{q}\right)p^{1-1}$$

Do the arithmetic.

$$\left(-\frac{5}{q}\right)p^{0}$$

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

$$\left(-\frac{5}{q}\right)\times 1$$

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

$$-\frac{5}{q}$$

Evaluate

$$-\frac{5p}{q}$$

Solution Steps

Cancel out 6p in both numerator and denominator.

$$\frac{-5p}{q}$$