Solve x*x*x*3*3*x*3*x=

$$x \cdot x \cdot x \cdot 3 \cdot 3 \cdot x \cdot 3 \cdot x =$$

Evaluate

$$27x^{5}$$

Solution Steps

Multiply x and x to get x^{2}.

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$x^{5}\times 3\times 3\times 3$$

Multiply 3 and 3 to get 9.

$$x^{5}\times 9\times 3$$

Multiply 9 and 3 to get 27.

$$x^{5}\times 27$$

Differentiate w.r.t. x

$$135x^{4}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 3\times 3\times 3x)$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}\times 3\times 3\times 3)$$

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}\times 9\times 3)$$

Multiply 9 and 3 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}\times 27)$$

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

$$5\times 27x^{5-1}$$

Multiply 5 times 27.

$$135x^{5-1}$$

Subtract 1 from 5.

$$135x^{4}$$