Solve 2x*{x}^frac{1{2}}

$$2x \times { x }^{ \frac{ 1 }{ 2 } }$$

Differentiate w.r.t. x

$$3\sqrt{x}$$

Steps Using Definition of a Derivative

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

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

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

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

Multiply \frac{3}{2} times 2.

$$3x^{\frac{3}{2}-1}$$

Subtract 1 from \frac{3}{2}.

$$3\sqrt{x}$$

Evaluate

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

Solution Steps

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

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