Solve 4^2+5^0x+1000^12

$$4 ^ { 2 } + 5 ^ { 0 } x + 1000 ^ { 12 }$$

Evaluate

$$x+1000000000000000000000000000000000016$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$16+5^{0}x+1000^{12}$$

Calculate 5 to the power of 0 and get 1.

$$16+1x+1000^{12}$$

Calculate 1000 to the power of 12 and get 1000000000000000000000000000000000000.

$$16+1x+1000000000000000000000000000000000000$$

Add 16 and 1000000000000000000000000000000000000 to get 1000000000000000000000000000000000016.

$$1000000000000000000000000000000000016+1x$$

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

$$1000000000000000000000000000000000016+x$$

Differentiate w.r.t. x

$$1$$

Steps Using Derivative Rule for Sum

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16+5^{0}x+1000^{12})$$

Calculate 5 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16+1x+1000^{12})$$

Calculate 1000 to the power of 12 and get 1000000000000000000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16+1x+1000000000000000000000000000000000000)$$

Add 16 and 1000000000000000000000000000000000000 to get 1000000000000000000000000000000000016.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1000000000000000000000000000000000016+1x)$$

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}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

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

$$1$$