Solve 7n^3/3n

$$\frac { 7 n ^ { 3 } } { 3 n }$$

Evaluate

$$\frac{7n^{2}}{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{7^{1}n^{3}}{3^{1}n^{1}}$$

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

$$\frac{7^{1}n^{3-1}}{3^{1}}$$

Subtract 1 from 3.

$$\frac{7^{1}n^{2}}{3^{1}}$$

Divide 7 by 3.

$$\frac{7}{3}n^{2}$$

Differentiate w.r.t. n

$$\frac{14n}{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{7}{3}n^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{7}{3}n^{2})$$

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}.

$$2\times \frac{7}{3}n^{2-1}$$

Do the arithmetic.

$$\frac{14}{3}n^{1}$$

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

$$\frac{14}{3}n$$