Solve 4x^2+1-2x2^n+1

$$4 x ^ { 2 } + 1 - 2 x 2 ^ { n + 1 }$$

Differentiate w.r.t. x

$$8x-4\times 2^{n}$$

Steps Using Derivative Rule for Sum

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}.

$$2\times 4x^{2-1}+\left(-2\times 2^{n+1}\right)x^{1-1}$$

Multiply 2 times 4.

$$8x^{2-1}+\left(-2\times 2^{n+1}\right)x^{1-1}$$

Subtract 1 from 2.

$$8x^{1}+\left(-2\times 2^{n+1}\right)x^{1-1}$$

Subtract 1 from 1.

$$8x^{1}+\left(-4\times 2^{n}\right)x^{0}$$

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

$$8x+\left(-4\times 2^{n}\right)x^{0}$$

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

$$8x+\left(-4\times 2^{n}\right)\times 1$$

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

$$8x-4\times 2^{n}$$

Evaluate

$$4x^{2}-4x\times 2^{n}+1$$