Solve 3/5sqrt{1}x1/4x^2

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

Evaluate

$$\frac{3x^{3}}{20}$$

Solution Steps

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

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

Calculate the square root of 1 and get 1.

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

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

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

Multiply \frac{3}{5} and \frac{1}{4} to get \frac{3}{20}.

$$\frac{3}{20}x^{3}$$

Differentiate w.r.t. x

$$\frac{9x^{2}}{20}$$

Steps Using Definition of a Derivative

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

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

Calculate the square root of 1 and get 1.

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

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

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

Multiply \frac{3}{5} and \frac{1}{4} to get \frac{3}{20}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{20}x^{3})$$

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

$$3\times \frac{3}{20}x^{3-1}$$

Multiply 3 times \frac{3}{20}.

$$\frac{9}{20}x^{3-1}$$

Subtract 1 from 3.

$$\frac{9}{20}x^{2}$$