Solve 10n^4/5n=

$$\frac { 10 n ^ { 4 } } { 5 n } =$$

Evaluate

$$2n^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}n^{4}}{5^{1}n^{1}}$$

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

$$\frac{10^{1}n^{4-1}}{5^{1}}$$

Subtract 1 from 4.

$$\frac{10^{1}n^{3}}{5^{1}}$$

Divide 10 by 5.

$$2n^{3}$$

Differentiate w.r.t. n

$$6n^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{10}{5}n^{4-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$6n^{2}$$