Solve x^3+1/15*x^3-0

$$x ^ { 3 } + \frac { 1 } { 15 } \cdot x ^ { 3 } - 0$$

Differentiate w.r.t. x

$$\frac{16x^{2}}{5}$$

Steps Using Definition of a Derivative

Combine x^{3} and \frac{1}{15}x^{3} to get \frac{16}{15}x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{15}x^{3}-0)$$

Multiply -1 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{15}x^{3}+0)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{15}x^{3})$$

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

$$3\times \frac{16}{15}x^{3-1}$$

Multiply 3 times \frac{16}{15}.

$$\frac{16}{5}x^{3-1}$$

Subtract 1 from 3.

$$\frac{16}{5}x^{2}$$

Evaluate

$$\frac{16x^{3}}{15}$$

Solution Steps

Combine x^{3} and \frac{1}{15}x^{3} to get \frac{16}{15}x^{3}.

$$\frac{16}{15}x^{3}-0$$