Solve (3)(x^4)^3div(x^2)^3

$$( 3 ) ( x ^ { 4 } ) ^ { 3 } \div ( x ^ { 2 } ) ^ { 3 }$$

Evaluate

$$3x^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{3x^{12}}{\left(x^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

Cancel out x^{6} in both numerator and denominator.

$$3x^{6}$$

Differentiate w.r.t. x

$$18x^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{12}}{\left(x^{2}\right)^{3}})$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{12}}{x^{6}})$$

Cancel out x^{6} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{6})$$

The derivative of ax^{n} is nax^{n-1}.

$$6\times 3x^{6-1}$$

Multiply 6 times 3.

$$18x^{6-1}$$

Subtract 1 from 6.

$$18x^{5}$$