Solve 2x^2*3x^2*x

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

Evaluate

$$6x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$2x^{4}\times 3x$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$2x^{5}\times 3$$

Multiply 2 and 3 to get 6.

$$6x^{5}$$

Differentiate w.r.t. x

$$30x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}\times 3x)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{5})$$

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

$$5\times 6x^{5-1}$$

Multiply 5 times 6.

$$30x^{5-1}$$

Subtract 1 from 5.

$$30x^{4}$$