Solve 2x^3*3x^5

$$2 x ^ { 3 } \times 3 x ^ { 5 }$$

Evaluate

$$6x^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$2x^{8}\times 3$$

Multiply 2 and 3 to get 6.

$$6x^{8}$$

Differentiate w.r.t. x

$$48x^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{8}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{8})$$

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

$$8\times 6x^{8-1}$$

Multiply 8 times 6.

$$48x^{8-1}$$

Subtract 1 from 8.

$$48x^{7}$$