Solve 21x^2/7x

$$\frac { 21 x ^ { 2 } } { 7 x }$$

Evaluate

$$3x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{21^{1}x^{2}}{7^{1}x^{1}}$$

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

$$\frac{21^{1}x^{2-1}}{7^{1}}$$

Subtract 1 from 2.

$$\frac{21^{1}x^{1}}{7^{1}}$$

Divide 21 by 7.

$$3x^{1}$$

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

$$3x$$

Differentiate w.r.t. x

$$3$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{21}{7}x^{2-1})$$

Do the arithmetic.

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

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}.

$$3x^{1-1}$$

Do the arithmetic.

$$3x^{0}$$

For any term t except 0, t^{0}=1.

$$3\times 1$$

For any term t, t\times 1=t and 1t=t.

$$3$$