Solve 6L^frac{1{2}}-L-1

$$6 L ^ { \frac { 1 } { 2 } } - L - 1$$

Differentiate w.r.t. L

$$-1+\frac{3}{\sqrt{L}}$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{1}{2}\times 6L^{\frac{1}{2}-1}-L^{1-1}$$

Multiply \frac{1}{2} times 6.

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

Subtract 1 from \frac{1}{2}.

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

Subtract 1 from 1.

$$3L^{-\frac{1}{2}}-L^{0}$$

For any term t except 0, t^{0}=1.

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

Evaluate

$$-L+6\sqrt{L}-1$$