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

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

Differentiate w.r.t. x

$$7x^{\frac{4}{3}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and \frac{1}{3} to get \frac{7}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{\frac{7}{3}})$$

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

$$\frac{7}{3}\times 3x^{\frac{7}{3}-1}$$

Multiply \frac{7}{3} times 3.

$$7x^{\frac{7}{3}-1}$$

Subtract 1 from \frac{7}{3}.

$$7x^{\frac{4}{3}}$$

Evaluate

$$3x^{\frac{7}{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and \frac{1}{3} to get \frac{7}{3}.

$$3x^{\frac{7}{3}}$$