Solve x*4!*2^4

$$x \cdot 4 ! \cdot 2 ^ { 4 }$$

Evaluate

$$384x$$

Solution Steps

The factorial of 4 is 24.

$$x\times 24\times 2^{4}$$

Calculate 2 to the power of 4 and get 16.

$$x\times 24\times 16$$

Multiply 24 and 16 to get 384.

$$x\times 384$$

Differentiate w.r.t. x

$$384$$

Steps Using Definition of a Derivative

The factorial of 4 is 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 24\times 2^{4})$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 24\times 16)$$

Multiply 24 and 16 to get 384.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 384)$$

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

$$384x^{1-1}$$

Subtract 1 from 1.

$$384x^{0}$$

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

$$384\times 1$$

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

$$384$$