Solve 4^2/3x(1^2x2^2)

$$\frac{ { 4 }^{ 2 } }{ 3 } x( { 1 }^{ 2 } x { 2 }^{ 2 } )$$

Evaluate

$$\frac{64x^{2}}{3}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{4^{2}}{3}x^{2}\times 1^{2}\times 2^{2}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16}{3}x^{2}\times 1^{2}\times 2^{2}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{16}{3}x^{2}\times 1\times 2^{2}$$

Multiply \frac{16}{3} and 1 to get \frac{16}{3}.

$$\frac{16}{3}x^{2}\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16}{3}x^{2}\times 4$$

Express \frac{16}{3}\times 4 as a single fraction.

$$\frac{16\times 4}{3}x^{2}$$

Multiply 16 and 4 to get 64.

$$\frac{64}{3}x^{2}$$

Differentiate w.r.t. x

$$\frac{128x}{3}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4^{2}}{3}x^{2}\times 1^{2}\times 2^{2})$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{3}x^{2}\times 1^{2}\times 2^{2})$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{3}x^{2}\times 1\times 2^{2})$$

Multiply \frac{16}{3} and 1 to get \frac{16}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{3}x^{2}\times 2^{2})$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16}{3}x^{2}\times 4)$$

Express \frac{16}{3}\times 4 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{16\times 4}{3}x^{2})$$

Multiply 16 and 4 to get 64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{64}{3}x^{2})$$

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

$$2\times \frac{64}{3}x^{2-1}$$

Multiply 2 times \frac{64}{3}.

$$\frac{128}{3}x^{2-1}$$

Subtract 1 from 2.

$$\frac{128}{3}x^{1}$$

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

$$\frac{128}{3}x$$