Solve 2x^2*3x^4

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

Evaluate

$$6x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

Multiply 2 and 3 to get 6.

$$6x^{6}$$

Differentiate w.r.t. x

$$36x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}\times 3)$$

Multiply 2 and 3 to get 6.

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

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

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

Multiply 6 times 6.

$$36x^{6-1}$$

Subtract 1 from 6.

$$36x^{5}$$