Solve d/dxleft(x^4-10x^3+x+1right)

$$\frac{d}{d x } \left( { x }^{ 4 } -10 { x }^{ 3 } +x+1 \right)$$

Evaluate

$$4x^{3}-30x^{2}+1$$

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}.

$$4x^{4-1}+3\left(-10\right)x^{3-1}+x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+3\left(-10\right)x^{3-1}+x^{1-1}$$

Multiply 3 times -10.

$$4x^{3}-30x^{3-1}+x^{1-1}$$

Subtract 1 from 3.

$$4x^{3}-30x^{2}+x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}-30x^{2}+x^{0}$$

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

$$4x^{3}-30x^{2}+1$$

Differentiate w.r.t. x

$$12x\left(x-5\right)$$