Solve 2/5kquad3/5+1/10k

$$\frac { 2 } { 5 } k \quad \frac { 3 } { 5 } + \frac { 1 } { 10 } k$$

Evaluate

$$\frac{17k}{50}$$

Solution Steps

Multiply \frac{2}{5} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 3}{5\times 5}k+\frac{1}{10}k$$

Do the multiplications in the fraction \frac{2\times 3}{5\times 5}.

$$\frac{6}{25}k+\frac{1}{10}k$$

Combine \frac{6}{25}k and \frac{1}{10}k to get \frac{17}{50}k.

$$\frac{17}{50}k$$

Differentiate w.r.t. k

$$\frac{17}{50} = 0.34$$

Steps Using Definition of a Derivative

Multiply \frac{2}{5} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{2\times 3}{5\times 5}k+\frac{1}{10}k)$$

Do the multiplications in the fraction \frac{2\times 3}{5\times 5}.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{6}{25}k+\frac{1}{10}k)$$

Combine \frac{6}{25}k and \frac{1}{10}k to get \frac{17}{50}k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{17}{50}k)$$

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

$$\frac{17}{50}k^{1-1}$$

Subtract 1 from 1.

$$\frac{17}{50}k^{0}$$

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

$$\frac{17}{50}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{17}{50}$$