Solve (21x^3/3x)

$$( \frac { 21 x ^ { 3 } } { 3 x } )$$

Evaluate

$$7x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{21^{1}x^{3}}{3^{1}x^{1}}$$

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

$$\frac{21^{1}x^{3-1}}{3^{1}}$$

Subtract 1 from 3.

$$\frac{21^{1}x^{2}}{3^{1}}$$

Divide 21 by 3.

$$7x^{2}$$

Differentiate w.r.t. x

$$14x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21}{3}x^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2})$$

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}.

$$2\times 7x^{2-1}$$

Do the arithmetic.

$$14x^{1}$$

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

$$14x$$