Solve 4x+x2^-20

$$4 x + x 2 ^ { - 20 }$$

Evaluate

$$\frac{4194305x}{1048576}$$

Solution Steps

Calculate 2 to the power of -20 and get \frac{1}{1048576}.

$$4x+x\times \frac{1}{1048576}$$

Combine 4x and x\times \frac{1}{1048576} to get \frac{4194305}{1048576}x.

$$\frac{4194305}{1048576}x$$

Differentiate w.r.t. x

$$\frac{4194305}{1048576} = 4\frac{1}{1048576} = 4.000000953674316$$

Steps Using Definition of a Derivative

Calculate 2 to the power of -20 and get \frac{1}{1048576}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+x\times \frac{1}{1048576})$$

Combine 4x and x\times \frac{1}{1048576} to get \frac{4194305}{1048576}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4194305}{1048576}x)$$

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

$$\frac{4194305}{1048576}x^{1-1}$$

Subtract 1 from 1.

$$\frac{4194305}{1048576}x^{0}$$

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

$$\frac{4194305}{1048576}\times 1$$

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

$$\frac{4194305}{1048576}$$