Solve 2left(x^3right)^2x^3

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

Evaluate

$$2x^{9}$$

Solution Steps

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

$$2x^{6}x^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$2x^{9}$$

Differentiate w.r.t. x

$$18x^{8}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}x^{3})$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{9})$$

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

$$9\times 2x^{9-1}$$

Multiply 9 times 2.

$$18x^{9-1}$$

Subtract 1 from 9.

$$18x^{8}$$