Solve (3/4)^3*n

$$( \frac { 3 } { 4 } ) ^ { 3 } \cdot n$$

Differentiate w.r.t. n

$$\frac{27}{64} = 0.421875$$

Steps Using Definition of a Derivative

Calculate \frac{3}{4} to the power of 3 and get \frac{27}{64}.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{27}{64}n)$$

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

$$\frac{27}{64}n^{1-1}$$

Subtract 1 from 1.

$$\frac{27}{64}n^{0}$$

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

$$\frac{27}{64}\times 1$$

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

$$\frac{27}{64}$$

Evaluate

$$\frac{27n}{64}$$

Solution Steps

Calculate \frac{3}{4} to the power of 3 and get \frac{27}{64}.

$$\frac{27}{64}n$$