Solve (2/5x)*(1/3x^2)*2,5x

$$( \frac { 2 } { 5 } x ) \cdot ( \frac { 1 } { 3 } x ^ { 2 } ) \cdot 2,5 x$$

Evaluate

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

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{2}{5}x^{4}\times \frac{1}{3}\times 2,5$$

Multiply \frac{2}{5} and \frac{1}{3} to get \frac{2}{15}.

$$\frac{2}{15}x^{4}\times 2,5$$

Multiply \frac{2}{15} and 2,5 to get \frac{1}{3}.

$$\frac{1}{3}x^{4}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{5}x^{3}\times \frac{1}{3}\times 2,5x)$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{5}x^{4}\times \frac{1}{3}\times 2,5)$$

Multiply \frac{2}{5} and \frac{1}{3} to get \frac{2}{15}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{15}x^{4}\times 2,5)$$

Multiply \frac{2}{15} and 2,5 to get \frac{1}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3}x^{4})$$

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

$$4\times \frac{1}{3}x^{4-1}$$

Multiply 4 times \frac{1}{3}.

$$\frac{4}{3}x^{4-1}$$

Subtract 1 from 4.

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