Solve 13c^9d^10/-26c^9d

$$\frac{ 13 { c }^{ 9 } { d }^{ 10 } }{ -26 { c }^{ 9 } d }$$

Evaluate

$$-\frac{d^{9}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{13^{1}c^{9}d^{10}}{\left(-26\right)^{1}c^{9}d^{1}}$$

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

$$\frac{13^{1}}{\left(-26\right)^{1}}c^{9-9}d^{10-1}$$

Subtract 9 from 9.

$$\frac{13^{1}}{\left(-26\right)^{1}}c^{0}d^{10-1}$$

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

$$\frac{13^{1}}{\left(-26\right)^{1}}d^{10-1}$$

Subtract 1 from 10.

$$\frac{13^{1}}{\left(-26\right)^{1}}d^{9}$$

Reduce the fraction \frac{13}{-26} to lowest terms by extracting and canceling out 13.

$$-\frac{1}{2}d^{9}$$

Differentiate w.r.t. d

$$-\frac{9d^{8}}{2}$$

Steps Using Definition of a Derivative

Cancel out 13dc^{9} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{d^{9}}{-2})$$

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

$$9\left(-\frac{1}{2}\right)d^{9-1}$$

Multiply 9 times -\frac{1}{2}.

$$-\frac{9}{2}d^{9-1}$$

Subtract 1 from 9.

$$-\frac{9}{2}d^{8}$$