Solve 7x^100-4x^99+26x^101-5

$$7 { x }^{ 100 } -4 { x }^{ 99 } +26 { x }^{ 101 } -5$$

Differentiate w.r.t. x

$$2\left(1313x^{2}+350x-198\right)x^{98}$$

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}.

$$100\times 7x^{100-1}+99\left(-4\right)x^{99-1}+101\times 26x^{101-1}$$

Multiply 100 times 7.

$$700x^{100-1}+99\left(-4\right)x^{99-1}+101\times 26x^{101-1}$$

Subtract 1 from 100.

$$700x^{99}+99\left(-4\right)x^{99-1}+101\times 26x^{101-1}$$

Multiply 99 times -4.

$$700x^{99}-396x^{99-1}+101\times 26x^{101-1}$$

Subtract 1 from 99.

$$700x^{99}-396x^{98}+101\times 26x^{101-1}$$

Multiply 99 times -4.

$$700x^{99}-396x^{98}+2626x^{101-1}$$

Subtract 1 from 101.

$$700x^{99}-396x^{98}+2626x^{100}$$

Evaluate

$$26x^{101}+7x^{100}-4x^{99}-5$$