Solve x*x^2*3x

$$x \cdot x^2 \cdot 3x$$

Evaluate

$$3x^{4}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$x^{4}\times 3$$

Differentiate w.r.t. x

$$12x^{3}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 3)$$

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

$$4\times 3x^{4-1}$$

Multiply 4 times 3.

$$12x^{4-1}$$

Subtract 1 from 4.

$$12x^{3}$$