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

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

Evaluate

$$18x^{8}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$6x^{8}\times 3$$

Multiply 6 and 3 to get 18.

$$18x^{8}$$

Differentiate w.r.t. x

$$144x^{7}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{8}\times 3)$$

Multiply 6 and 3 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{8})$$

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

$$8\times 18x^{8-1}$$

Multiply 8 times 18.

$$144x^{8-1}$$

Subtract 1 from 8.

$$144x^{7}$$