Solve 11c^2d^2/121cd

$$\frac { 11 c ^ { 2 } d ^ { 2 } } { 121 c d }$$

Evaluate

$$\frac{cd}{11}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{11^{1}c^{2}d^{2}}{121^{1}c^{1}d^{1}}$$

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

$$\frac{11^{1}}{121^{1}}c^{2-1}d^{2-1}$$

Subtract 1 from 2.

$$\frac{11^{1}}{121^{1}}c^{1}d^{2-1}$$

Subtract 1 from 2.

$$\frac{11^{1}}{121^{1}}cd^{1}$$

Reduce the fraction \frac{11}{121} to lowest terms by extracting and canceling out 11.

$$\frac{1}{11}cd$$

Differentiate w.r.t. c

$$\frac{d}{11}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{11d^{2}}{121d}c^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{d}{11}c^{1})$$

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}.

$$\frac{d}{11}c^{1-1}$$

Do the arithmetic.

$$\frac{d}{11}c^{0}$$

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

$$\frac{d}{11}\times 1$$

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

$$\frac{d}{11}$$