Solve 9x^4/3x^1=

$$\frac { 9 x ^ { 4 } } { 3 x ^ { 1 } } =$$

Evaluate

$$3x^{3}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{9^{1}x^{4}}{3^{1}x^{1}}$$

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

$$\frac{9^{1}x^{4-1}}{3^{1}}$$

Subtract 1 from 4.

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

Divide 9 by 3.

$$3x^{3}$$

Differentiate w.r.t. x

$$9x^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{3}x^{4-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$9x^{2}$$