Solve x^1*2^3

$$x ^ { 1 } \cdot 2 ^ { 3 }$$

Evaluate

$$8x$$

Solution Steps

Calculate x to the power of 1 and get x.

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

Calculate 2 to the power of 3 and get 8.

$$x\times 8$$

Differentiate w.r.t. x

$$8$$

Steps Using Definition of a Derivative

Calculate x to the power of 1 and get x.

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

Calculate 2 to the power of 3 and get 8.

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

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

$$8x^{1-1}$$

Subtract 1 from 1.

$$8x^{0}$$

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

$$8\times 1$$

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

$$8$$