Solve x^2*3x*6x^3

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

Evaluate

$$18x^{6}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Multiply 3 and 6 to get 18.

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

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 1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Multiply 3 and 6 to get 18.

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

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.

$$108x^{5}$$