Solve 7w^5n^5/35w^2n^4

$$\frac { 7 w ^ { 5 } n ^ { 5 } } { 35 w ^ { 2 } n ^ { 4 } }$$

Evaluate

$$\frac{nw^{3}}{5}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{7^{1}w^{5}n^{5}}{35^{1}w^{2}n^{4}}$$

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

$$\frac{7^{1}}{35^{1}}w^{5-2}n^{5-4}$$

Subtract 2 from 5.

$$\frac{7^{1}}{35^{1}}w^{3}n^{5-4}$$

Subtract 4 from 5.

$$\frac{7^{1}}{35^{1}}w^{3}n^{1}$$

Reduce the fraction \frac{7}{35} to lowest terms by extracting and canceling out 7.

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

Differentiate w.r.t. w

$$\frac{3nw^{2}}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{7n^{5}}{35n^{4}}w^{5-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}w}(\frac{n}{5}w^{3})$$

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}.

$$3\times \frac{n}{5}w^{3-1}$$

Do the arithmetic.

$$\frac{3n}{5}w^{2}$$