Solve (x^2)^3(x^5)

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

Evaluate

$$x^{11}$$

Solution Steps

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

$$x^{6}x^{5}$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$x^{11}$$

Differentiate w.r.t. x

$$11x^{10}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{6}x^{5})$$

To multiply powers of the same base, add their exponents. Add 6 and 5 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{11})$$

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

$$11x^{11-1}$$

Subtract 1 from 11.

$$11x^{10}$$