Solve 2x^frac{3{5}}*9x^2

$$2 x ^ { \frac { 3 } { 5 } } \cdot 9 x ^ { 2 }$$

Evaluate

$$18x^{\frac{13}{5}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add \frac{3}{5} and 2 to get \frac{13}{5}.

$$2x^{\frac{13}{5}}\times 9$$

Multiply 2 and 9 to get 18.

$$18x^{\frac{13}{5}}$$

Differentiate w.r.t. x

$$\frac{234x^{\frac{8}{5}}}{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add \frac{3}{5} and 2 to get \frac{13}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{\frac{13}{5}}\times 9)$$

Multiply 2 and 9 to get 18.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{\frac{13}{5}})$$

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

$$\frac{13}{5}\times 18x^{\frac{13}{5}-1}$$

Multiply \frac{13}{5} times 18.

$$\frac{234}{5}x^{\frac{13}{5}-1}$$

Subtract 1 from \frac{13}{5}.

$$\frac{234}{5}x^{\frac{8}{5}}$$