Solve 6x^7*3x^9

$$6 { x }^{ 7 } \times 3 { x }^{ 9 }$$

Evaluate

$$18x^{16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 9 to get 16.

$$6x^{16}\times 3$$

Multiply 6 and 3 to get 18.

$$18x^{16}$$

Differentiate w.r.t. x

$$288x^{15}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 9 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{16}\times 3)$$

Multiply 6 and 3 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{16})$$

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

$$16\times 18x^{16-1}$$

Multiply 16 times 18.

$$288x^{16-1}$$

Subtract 1 from 16.

$$288x^{15}$$