Solve 32x^3/20x

$$\frac { 32 x ^ { 3 } } { 20 x }$$

Evaluate

$$\frac{8x^{2}}{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{32^{1}x^{3}}{20^{1}x^{1}}$$

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

$$\frac{32^{1}x^{3-1}}{20^{1}}$$

Subtract 1 from 3.

$$\frac{32^{1}x^{2}}{20^{1}}$$

Reduce the fraction \frac{32}{20} to lowest terms by extracting and canceling out 4.

$$\frac{8}{5}x^{2}$$

Differentiate w.r.t. x

$$\frac{16x}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{32}{20}x^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8}{5}x^{2})$$

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}.

$$2\times \frac{8}{5}x^{2-1}$$

Do the arithmetic.

$$\frac{16}{5}x^{1}$$

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

$$\frac{16}{5}x$$