Solve n-1/55/1+5n/1

$$n- \frac{ 1 }{ 5 } \frac{ 5 }{ 1 } + \frac{ 5n }{ 1 }$$

Evaluate

$$6n-1$$

Solution Steps

Anything divided by one gives itself.

$$n-\frac{1}{5}\times 5+\frac{5n}{1}$$

Cancel out 5 and 5.

$$n-1+\frac{5n}{1}$$

Anything divided by one gives itself.

$$n-1+5n$$

Combine n and 5n to get 6n.

$$6n-1$$

Differentiate w.r.t. n

$$6$$

Steps Using Derivative Rule for Sum

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n-\frac{1}{5}\times 5+\frac{5n}{1})$$

Cancel out 5 and 5.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n-1+\frac{5n}{1})$$

Anything divided by one gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n-1+5n)$$

Combine n and 5n to get 6n.

$$\frac{\mathrm{d}}{\mathrm{d}n}(6n-1)$$

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}.

$$6n^{1-1}$$

Subtract 1 from 1.

$$6n^{0}$$

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

$$6\times 1$$

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

$$6$$