Solve 3x^2*2x^4

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

Evaluate

$$6x^{6}$$

Solution Steps

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

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

Multiply 3 and 2 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.

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

Multiply 3 and 2 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.

$$36x^{5}$$