Solve 3x(3/4)^3

$$3 x ( \frac { 3 } { 4 } ) ^ { 3 }$$

Evaluate

$$\frac{81x}{64}$$

Solution Steps

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

$$3x\times \frac{27}{64}$$

Express 3\times \frac{27}{64} as a single fraction.

$$\frac{3\times 27}{64}x$$

Multiply 3 and 27 to get 81.

$$\frac{81}{64}x$$

Differentiate w.r.t. x

$$\frac{81}{64} = 1\frac{17}{64} = 1.265625$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x\times \frac{27}{64})$$

Express 3\times \frac{27}{64} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 27}{64}x)$$

Multiply 3 and 27 to get 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{81}{64}x)$$

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

$$\frac{81}{64}x^{1-1}$$

Subtract 1 from 1.

$$\frac{81}{64}x^{0}$$

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

$$\frac{81}{64}\times 1$$

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

$$\frac{81}{64}$$