Solve 27x^3/9x

$$\frac{ 27 { x }^{ 3 } }{ 9x }$$

Evaluate

$$3x^{2}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{27^{1}x^{3}}{9^{1}x^{1}}$$

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

$$\frac{27^{1}x^{3-1}}{9^{1}}$$

Subtract 1 from 3.

$$\frac{27^{1}x^{2}}{9^{1}}$$

Divide 27 by 9.

$$3x^{2}$$

Differentiate w.r.t. x

$$6x$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{27}{9}x^{3-1})$$

Do the arithmetic.

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

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}.

$$2\times 3x^{2-1}$$

Do the arithmetic.

$$6x^{1}$$

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

$$6x$$