Solve x:9:8:64

$$x : 9 : 8 : 64$$

Evaluate

$$\frac{x}{4608}$$

Solution Steps

Express \frac{\frac{\frac{x}{9}}{8}}{64} as a single fraction.

$$\frac{\frac{x}{9}}{8\times 64}$$

Multiply 8 and 64 to get 512.

$$\frac{\frac{x}{9}}{512}$$

Express \frac{\frac{x}{9}}{512} as a single fraction.

$$\frac{x}{9\times 512}$$

Multiply 9 and 512 to get 4608.

$$\frac{x}{4608}$$

Differentiate w.r.t. x

$$\frac{1}{4608} = 0.00021701388888888888$$

Steps Using Definition of a Derivative

Express \frac{\frac{\frac{x}{9}}{8}}{64} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{9}}{8\times 64})$$

Multiply 8 and 64 to get 512.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{9}}{512})$$

Express \frac{\frac{x}{9}}{512} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{9\times 512})$$

Multiply 9 and 512 to get 4608.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{4608})$$

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

$$\frac{1}{4608}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{4608}x^{0}$$

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

$$\frac{1}{4608}\times 1$$

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

$$\frac{1}{4608}$$