Solve (x^3)^3*x^3

$$( x ^ { 3 } ) ^ { 3 } \cdot x ^ { 3 }$$

Evaluate

$$x^{12}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$x^{9}x^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

$$x^{12}$$

Differentiate w.r.t. x

$$12x^{11}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

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

To multiply powers of the same base, add their exponents. Add 9 and 3 to get 12.

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

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

$$12x^{12-1}$$

Subtract 1 from 12.

$$12x^{11}$$