Solve (x)^2+(4^2)^2

$$( x ) ^ { 2 } + ( 4 ^ { 2 } ) ^ { 2 }$$

Evaluate

$$x^{2}+256$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate 4 to the power of 4 and get 256.

$$x^{2}+256$$

Differentiate w.r.t. x

$$2x$$

Steps Using Derivative Rule for Sum

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

Calculate 4 to the power of 4 and get 256.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+256)$$

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}.

$$2x^{2-1}$$

Subtract 1 from 2.

$$2x^{1}$$

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

$$2x$$