Solve 3r^3/2r

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

Evaluate

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

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{3^{1}r^{3}}{2^{1}r^{1}}$$

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

$$\frac{3^{1}r^{3-1}}{2^{1}}$$

Subtract 1 from 3.

$$\frac{3^{1}r^{2}}{2^{1}}$$

Divide 3 by 2.

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

Differentiate w.r.t. r

$$3r$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{3}{2}r^{3-1})$$

Do the arithmetic.

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

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}.

$$2\times \frac{3}{2}r^{2-1}$$

Do the arithmetic.

$$3r^{1}$$

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

$$3r$$