Solve (3x^2)(x^-1)

$$( 3 x ^ { 2 } ) ( x ^ { - 1 } )$$

Evaluate

$$3x$$

Solution Steps

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

$$3x^{1}$$

Calculate x to the power of 1 and get x.

$$3x$$

Differentiate w.r.t. x

$$3$$

Steps Using Definition of a Derivative

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

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

Calculate x to the power of 1 and get x.

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

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

$$3x^{1-1}$$

Subtract 1 from 1.

$$3x^{0}$$

For any term t except 0, t^{0}=1.

$$3\times 1$$

For any term t, t\times 1=t and 1t=t.

$$3$$