Solve 1^2x^2/16^2/64*16

$$\frac { 1 ^ { 2 } x ^ { 2 } / 16 ^ { 2 } } { 64 \times 16 }$$

Evaluate

$$\frac{x^{2}}{262144}$$

Short Solution Steps

Calculate 1 to the power of 2 and get 1.

$$\frac{\frac{1x^{2}}{16^{2}}}{64\times 16}$$

Calculate 16 to the power of 2 and get 256.

$$\frac{\frac{1x^{2}}{256}}{64\times 16}$$

Multiply 64 and 16 to get 1024.

$$\frac{\frac{1x^{2}}{256}}{1024}$$

Express \frac{\frac{1x^{2}}{256}}{1024} as a single fraction.

$$\frac{1x^{2}}{256\times 1024}$$

Cancel out 1 in both numerator and denominator.

$$\frac{x^{2}}{256\times 1024}$$

Multiply 256 and 1024 to get 262144.

$$\frac{x^{2}}{262144}$$

Differentiate w.r.t. x

$$\frac{x}{131072}$$

Steps Using Definition of a Derivative

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1x^{2}}{16^{2}}}{64\times 16})$$

Calculate 16 to the power of 2 and get 256.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1x^{2}}{256}}{64\times 16})$$

Multiply 64 and 16 to get 1024.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1x^{2}}{256}}{1024})$$

Express \frac{\frac{1x^{2}}{256}}{1024} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1x^{2}}{256\times 1024})$$

Cancel out 1 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{256\times 1024})$$

Multiply 256 and 1024 to get 262144.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{262144})$$

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

$$2\times \frac{1}{262144}x^{2-1}$$

Multiply 2 times \frac{1}{262144}.

$$\frac{1}{131072}x^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{131072}x^{1}$$

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

$$\frac{1}{131072}x$$