Solve 12n^5/36n^1

$$\frac{ 12 { n }^{ 5 } }{ 36 { n }^{ 1 } }$$

Evaluate

$$\frac{n^{4}}{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}n^{5}}{36^{1}n^{1}}$$

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

$$\frac{12^{1}n^{5-1}}{36^{1}}$$

Subtract 1 from 5.

$$\frac{12^{1}n^{4}}{36^{1}}$$

Reduce the fraction \frac{12}{36} to lowest terms by extracting and canceling out 12.

$$\frac{1}{3}n^{4}$$

Differentiate w.r.t. n

$$\frac{4n^{3}}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{12}{36}n^{5-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{3}n^{4})$$

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}.

$$4\times \frac{1}{3}n^{4-1}$$

Do the arithmetic.

$$\frac{4}{3}n^{3}$$