Solve d/dx[5x^4-x^3+2x+pi]

$$\frac { d } { d x } [ 5 x ^ { 4 } - x ^ { 3 } + 2 x + \pi ]$$

Evaluate

$$20x^{3}-3x^{2}+2$$

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}.

$$4\times 5x^{4-1}+3\left(-1\right)x^{3-1}+2x^{1-1}$$

Multiply 4 times 5.

$$20x^{4-1}+3\left(-1\right)x^{3-1}+2x^{1-1}$$

Subtract 1 from 4.

$$20x^{3}+3\left(-1\right)x^{3-1}+2x^{1-1}$$

Multiply 3 times -1.

$$20x^{3}-3x^{3-1}+2x^{1-1}$$

Subtract 1 from 3.

$$20x^{3}-3x^{2}+2x^{1-1}$$

Subtract 1 from 1.

$$20x^{3}-3x^{2}+2x^{0}$$

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

$$20x^{3}-3x^{2}+2\times 1$$

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

$$20x^{3}-3x^{2}+2$$

Differentiate w.r.t. x

$$6x\left(10x-1\right)$$