Solve x^2(x^5)^3

$$x ^ { 2 } ( x ^ { 5 } ) ^ { 3 }$$

Evaluate

$$x^{17}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$x^{2}x^{15}$$

To multiply powers of the same base, add their exponents. Add 2 and 15 to get 17.

$$x^{17}$$

Differentiate w.r.t. x

$$17x^{16}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}x^{15})$$

To multiply powers of the same base, add their exponents. Add 2 and 15 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{17})$$

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

$$17x^{17-1}$$

Subtract 1 from 17.

$$17x^{16}$$