Solve 5x^4+3x^3-2x^2+3

$$5 x ^ { 4 } + 3 x ^ { 3 } - 2 x ^ { 2 } + 3$$

Differentiate w.r.t. x

$$x\left(20x^{2}+9x-4\right)$$

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}.

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

Multiply 4 times 5.

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

Subtract 1 from 4.

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

Multiply 3 times 3.

$$20x^{3}+9x^{3-1}+2\left(-2\right)x^{2-1}$$

Subtract 1 from 3.

$$20x^{3}+9x^{2}+2\left(-2\right)x^{2-1}$$

Multiply 3 times 3.

$$20x^{3}+9x^{2}-4x^{2-1}$$

Subtract 1 from 2.

$$20x^{3}+9x^{2}-4x^{1}$$

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

$$20x^{3}+9x^{2}-4x$$

Evaluate

$$5x^{4}+3x^{3}-2x^{2}+3$$