Solve 12x^7/3x

$$\frac { 12 x ^ { 7 } } { 3 x }$$

Evaluate

$$4x^{6}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{12^{1}x^{7}}{3^{1}x^{1}}$$

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

$$\frac{12^{1}x^{7-1}}{3^{1}}$$

Subtract 1 from 7.

$$\frac{12^{1}x^{6}}{3^{1}}$$

Divide 12 by 3.

$$4x^{6}$$

Differentiate w.r.t. x

$$24x^{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{12}{3}x^{7-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{6})$$

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}.

$$6\times 4x^{6-1}$$

Do the arithmetic.

$$24x^{5}$$