Solve 3x^2*6x^4

$$3 x ^ { 2 } \times 6 x ^ { 4 }$$

Evaluate

$$18x^{6}$$

Solution Steps

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

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

Multiply 3 and 6 to get 18.

$$18x^{6}$$

Differentiate w.r.t. x

$$108x^{5}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and 6 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{6})$$

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

$$6\times 18x^{6-1}$$

Multiply 6 times 18.

$$108x^{6-1}$$

Subtract 1 from 6.

$$108x^{5}$$