Solve (-3{x}^frac{1{2}})*(-3{x}^frac{1{2}})

$$(-3 { x }^{ \frac{ 1 }{ 2 } } ) \times (-3 { x }^{ \frac{ 1 }{ 2 } } )$$

Evaluate

$$9x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{1}{2} to get 1.

$$-3x^{1}\left(-3\right)$$

Calculate x to the power of 1 and get x.

$$-3x\left(-3\right)$$

Multiply -3 and -3 to get 9.

$$9x$$

Differentiate w.r.t. x

$$9$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{1}{2} and \frac{1}{2} to get 1.

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

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x\left(-3\right))$$

Multiply -3 and -3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x)$$

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

$$9x^{1-1}$$

Subtract 1 from 1.

$$9x^{0}$$

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

$$9\times 1$$

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

$$9$$