Solve 3x^2*6x^7

$$3 x ^ { 2 } \cdot 6 x ^ { 7 }$$

Evaluate

$$18x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

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

Multiply 3 and 6 to get 18.

$$18x^{9}$$

Differentiate w.r.t. x

$$162x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 7 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{9}\times 6)$$

Multiply 3 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{9})$$

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

$$9\times 18x^{9-1}$$

Multiply 9 times 18.

$$162x^{9-1}$$

Subtract 1 from 9.

$$162x^{8}$$