Solve 3x^2*x^frac{1{2}}

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

Differentiate w.r.t. x

$$\frac{15x^{\frac{3}{2}}}{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and \frac{1}{2} to get \frac{5}{2}.

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

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

$$\frac{5}{2}\times 3x^{\frac{5}{2}-1}$$

Multiply \frac{5}{2} times 3.

$$\frac{15}{2}x^{\frac{5}{2}-1}$$

Subtract 1 from \frac{5}{2}.

$$\frac{15}{2}x^{\frac{3}{2}}$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and \frac{1}{2} to get \frac{5}{2}.

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