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

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

Evaluate

$$6x^{5}$$

Solution Steps

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

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

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

$$x^{5}\times 3\times 2$$

Multiply 3 and 2 to get 6.

$$x^{5}\times 6$$

Differentiate w.r.t. x

$$30x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}x\times 3\times 2)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}\times 3\times 2)$$

Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}\times 6)$$

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

$$5\times 6x^{5-1}$$

Multiply 5 times 6.

$$30x^{5-1}$$

Subtract 1 from 5.

$$30x^{4}$$