Solve x*3x^3*1x^1

$$x \times 3 x ^ { 3 } \times 1 x ^ { 1 }$$

Evaluate

$$3x^{5}$$

Solution Steps

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

$$x^{4}\times 3\times 1x^{1}$$

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

$$x^{5}\times 3\times 1$$

Multiply 3 and 1 to get 3.

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

Differentiate w.r.t. x

$$15x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 3\times 1x^{1})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}\times 3\times 1)$$

Multiply 3 and 1 to get 3.

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

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

$$5\times 3x^{5-1}$$

Multiply 5 times 3.

$$15x^{5-1}$$

Subtract 1 from 5.

$$15x^{4}$$