Solve 3x*6x^2

$$3x \times 6 { x }^{ 2 }$$

Evaluate

$$18x^{3}$$

Solution Steps

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

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

Multiply 3 and 6 to get 18.

$$18x^{3}$$

Differentiate w.r.t. x

$$54x^{2}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{3})$$

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

$$3\times 18x^{3-1}$$

Multiply 3 times 18.

$$54x^{3-1}$$

Subtract 1 from 3.

$$54x^{2}$$