Solve -35mn^2div(7mn)

$$- 35 m n ^ { 2 } \div ( 7 m n )$$

Evaluate

$$-5n$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-35\right)^{1}m^{1}n^{2}}{7^{1}m^{1}n^{1}}$$

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

$$\frac{\left(-35\right)^{1}}{7^{1}}m^{1-1}n^{2-1}$$

Subtract 1 from 1.

$$\frac{\left(-35\right)^{1}}{7^{1}}m^{0}n^{2-1}$$

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

$$\frac{\left(-35\right)^{1}}{7^{1}}n^{2-1}$$

Subtract 1 from 2.

$$\frac{\left(-35\right)^{1}}{7^{1}}n^{1}$$

Divide -35 by 7.

$$-5n$$

Differentiate w.r.t. n

$$-5$$

Steps Using Definition of a Derivative

Cancel out 7mn in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}n}(-5n)$$

The derivative of ax^{n} is nax^{n-1}.

$$-5n^{1-1}$$

Subtract 1 from 1.

$$-5n^{0}$$

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

$$-5$$