Solve left(2xright)^1+2-2^2+2

$${ \left(2x \right) }^{ 1+2 } - { 2 }^{ 2+2 }$$

Evaluate

$$8\left(x^{3}-2\right)$$

Solution Steps

Add 1 and 2 to get 3.

$$\left(2x\right)^{3}-2^{2+2}$$

Expand \left(2x\right)^{3}.

$$2^{3}x^{3}-2^{2+2}$$

Calculate 2 to the power of 3 and get 8.

$$8x^{3}-2^{2+2}$$

Add 2 and 2 to get 4.

$$8x^{3}-2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$8x^{3}-16$$

Differentiate w.r.t. x

$$24x^{2}$$

Steps Using Derivative Rule for Sum

Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(2x\right)^{3}-2^{2+2})$$

Expand \left(2x\right)^{3}.

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

Calculate 2 to the power of 3 and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{3}-2^{2+2})$$

Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{3}-2^{4})$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{3}-16)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times 8x^{3-1}$$

Multiply 3 times 8.

$$24x^{3-1}$$

Subtract 1 from 3.

$$24x^{2}$$