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

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

Evaluate

$$3x^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$x^{8}\times 3x^{3}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$x^{11}\times 3$$

Differentiate w.r.t. x

$$33x^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}\times 3x^{3})$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{11}\times 3)$$

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

$$11\times 3x^{11-1}$$

Multiply 11 times 3.

$$33x^{11-1}$$

Subtract 1 from 11.

$$33x^{10}$$