Solve frac{sqrt{4}*b^2}{6}

$$\frac { \sqrt { 4 } \times b ^ { 2 } } { 6 }$$

Evaluate

$$\frac{b^{2}}{3}$$

Solution Steps

Calculate the square root of 4 and get 2.

$$\frac{2b^{2}}{6}$$

Divide 2b^{2} by 6 to get \frac{1}{3}b^{2}.

$$\frac{1}{3}b^{2}$$

Differentiate w.r.t. b

$$\frac{2b}{3}$$

Steps Using Definition of a Derivative

Calculate the square root of 4 and get 2.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{2b^{2}}{6})$$

Divide 2b^{2} by 6 to get \frac{1}{3}b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{3}b^{2})$$

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

$$2\times \frac{1}{3}b^{2-1}$$

Multiply 2 times \frac{1}{3}.

$$\frac{2}{3}b^{2-1}$$

Subtract 1 from 2.

$$\frac{2}{3}b^{1}$$

For any term t, t^{1}=t.

$$\frac{2}{3}b$$