Solve 0.1*6{k}^frac{1{2}}

$$0.1 \cdot 6 { k }^{ \frac{ 1 }{ 2 } }$$

Differentiate w.r.t. k

$$\frac{3}{10\sqrt{k}}$$

Steps Using Definition of a Derivative

Multiply 0.1 and 6 to get 0.6.

$$\frac{\mathrm{d}}{\mathrm{d}k}(0.6k^{\frac{1}{2}})$$

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

$$\frac{1}{2}\times 0.6k^{\frac{1}{2}-1}$$

Multiply \frac{1}{2} times 0.6 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{3}{10}k^{\frac{1}{2}-1}$$

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

$$\frac{3}{10}k^{-\frac{1}{2}}$$

Evaluate

$$\frac{3\sqrt{k}}{5}$$

Solution Steps

Multiply 0.1 and 6 to get 0.6.

$$0.6k^{\frac{1}{2}}$$