Solve x:4:32:16

$$x : 4 : 32 : 16$$

Evaluate

$$\frac{x}{2048}$$

Solution Steps

Express \frac{\frac{\frac{x}{4}}{32}}{16} as a single fraction.

$$\frac{\frac{x}{4}}{32\times 16}$$

Multiply 32 and 16 to get 512.

$$\frac{\frac{x}{4}}{512}$$

Express \frac{\frac{x}{4}}{512} as a single fraction.

$$\frac{x}{4\times 512}$$

Multiply 4 and 512 to get 2048.

$$\frac{x}{2048}$$

Differentiate w.r.t. x

$$\frac{1}{2048} = 0.00048828125$$

Steps Using Definition of a Derivative

Express \frac{\frac{\frac{x}{4}}{32}}{16} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{4}}{32\times 16})$$

Multiply 32 and 16 to get 512.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x}{4}}{512})$$

Express \frac{\frac{x}{4}}{512} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{4\times 512})$$

Multiply 4 and 512 to get 2048.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{2048})$$

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

$$\frac{1}{2048}x^{1-1}$$

Subtract 1 from 1.

$$\frac{1}{2048}x^{0}$$

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

$$\frac{1}{2048}\times 1$$

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

$$\frac{1}{2048}$$