Solve x^2*(x^3)^6

$$x ^ { 2 } \cdot ( x ^ { 3 } ) ^ { 6 }$$

Evaluate

$$x^{20}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$x^{2}x^{18}$$

To multiply powers of the same base, add their exponents. Add 2 and 18 to get 20.

$$x^{20}$$

Differentiate w.r.t. x

$$20x^{19}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{18})$$

To multiply powers of the same base, add their exponents. Add 2 and 18 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{20})$$

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

$$20x^{20-1}$$

Subtract 1 from 20.

$$20x^{19}$$