Solve 3x*3x^2

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

Evaluate

$$9x^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply 3 and 3 to get 9.

$$9x^{3}$$

Differentiate w.r.t. x

$$27x^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Multiply 3 and 3 to get 9.

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

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

$$3\times 9x^{3-1}$$

Multiply 3 times 9.

$$27x^{3-1}$$

Subtract 1 from 3.

$$27x^{2}$$