Solve 12v^5/32v

$$\frac { 12 v ^ { 5 } } { 32 v }$$

Evaluate

$$\frac{3v^{4}}{8}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}v^{5}}{32^{1}v^{1}}$$

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

$$\frac{12^{1}v^{5-1}}{32^{1}}$$

Subtract 1 from 5.

$$\frac{12^{1}v^{4}}{32^{1}}$$

Reduce the fraction \frac{12}{32} to lowest terms by extracting and canceling out 4.

$$\frac{3}{8}v^{4}$$

Differentiate w.r.t. v

$$\frac{3v^{3}}{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{12}{32}v^{5-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{3}{8}v^{4})$$

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}.

$$4\times \frac{3}{8}v^{4-1}$$

Do the arithmetic.

$$\frac{3}{2}v^{3}$$